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question_answer1)
Find the fourth vertex of the parallelogram if three of its vertices are given as A (10, - 2), B (8, 6) and C (6, 10).
A)
(0, 1) done
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B)
(- 2, 5) done
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C)
(4, 18) done
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D)
(8, 2) done
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question_answer2)
The point on the line \[3x-4y=25\], which is nearest to the origin is given by:
A)
(3, - 4) done
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B)
(- 3, - 4) done
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C)
(3, 4) done
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D)
(5, - 6) done
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question_answer3)
The points on x-axis which are at a distance of \[\sqrt{13}\] units from (- 2, 3) is____.
A)
(0, 0), (- 2, - 3) done
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B)
(0, 0), (- 4, 0) done
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C)
(0, 0), (2, 3) done
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D)
None of these done
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question_answer4)
Find the area of the triangle formed by the line\[5x-3y+15=0\] with coordinate axes.
A)
15 Sq. unit done
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B)
5 Sq. unit done
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C)
8 Sq. unit done
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D)
\[\frac{15}{2}\]Sq. unit done
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question_answer5)
The ratio in which the line joining points (a + b, b + a) and (a - b, b - a) is divided by point (a, b) is _____
A)
\[b:a\] internally done
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B)
\[1:1\]internally done
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C)
\[a:b\] internally done
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D)
\[2:1\]internally done
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question_answer6)
In what ratio does the line \[4x+3y-13=0\] divide the line segment joining the points (2, 1) and (1, 4)?
A)
\[3:2\] internally done
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B)
\[2:3\]internally done
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C)
\[2:3\] externally done
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D)
\[3:2\]externally done
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question_answer7)
Find the radius of the circle which passes through the origin, (0, 4) and (4, 0).
A)
\[2\] done
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B)
\[4\sqrt{2}\] done
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C)
\[\sqrt{8}\] done
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D)
\[3\sqrt{2}\] done
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question_answer8)
Find the circum-centre of the triangle whose vertices are \[(0,\text{ }0),\text{ (}3,\text{ }\sqrt{3})\] and \[(0,2\sqrt{3})\] .
A)
\[(1,\sqrt{3})\] done
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B)
\[(\sqrt{3},\sqrt{3})\] done
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C)
\[(2\sqrt{3},1)\] done
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D)
\[(2,\sqrt{3})\] done
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question_answer9)
What are the coordinates of the centroid of the triangle whose vertices are (6, 9), (5, 7) and (4, 10)?
A)
\[(3,9)\] done
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B)
\[(4,9)\] done
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C)
\[(6,8)\] done
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D)
\[\left( 5,8\frac{2}{3} \right)\] done
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question_answer10)
Find the centroid of the triangle whose vertices are (- 3, 2), (1, 5) and (11, - 19).
A)
(3, 4) done
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B)
(3, - 4) done
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C)
(- 3, - 4) done
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D)
(- 3. 4) done
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question_answer11)
The coordinates of the third vertex of an equilateral triangle whose two vertices are at (3, 4) (- 2, 3) are______.
A)
\[(1,7)\] done
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B)
\[(5,1)\] done
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C)
\[\left( \frac{1+\sqrt{3}}{2},\frac{7-5\sqrt{3}}{2} \right)\] or \[\left( \frac{1-\sqrt{3}}{2},\frac{7+5\sqrt{3}}{2} \right)\] done
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D)
\[(-5,5)\] done
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question_answer12)
The extremities of the diagonal of a parallelogram are the points (3, - 4) and (- 6, 5). Third vertex is the point (- 2, 1). Find its fourth vertex.
A)
(1, 1) done
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B)
(1, 0) done
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C)
(0, 1) done
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D)
(- 1, 0) done
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question_answer13)
Find the distance between the points \[\left( \sqrt{3}+1,\sqrt{2}-1 \right)\] and \[\left( \sqrt{3}-1,\sqrt{2}+1 \right)\].
A)
\[\sqrt{3}\] done
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B)
\[2\sqrt{3}\] done
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C)
\[\sqrt{2}\] done
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D)
\[2\sqrt{2}\] done
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question_answer14)
Vertices of a triangle ABC are A (2, 2), B (-4, -4) and C (5, - 8). Find the length of the median through C.
A)
\[\sqrt{65}\] done
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B)
\[\sqrt{117}\] done
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C)
\[\sqrt{85}\] done
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D)
\[\sqrt{113}\] done
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question_answer15)
If the points (a, 0), (0, b) and (1, 1) are collinear, which of the following is true?
A)
\[\frac{1}{a}+\frac{1}{b}=2\] done
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B)
\[\frac{1}{a}-\frac{1}{b}=1\] done
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C)
\[\frac{1}{a}-\frac{1}{b}=2\] done
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D)
\[\frac{1}{a}+\frac{1}{b}=1\] done
clear
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question_answer16)
Find the coordinates of the centroid or the triangle with vertices A (a, 0), B (0, b) and C (1, 1).
A)
\[(0,a)\] done
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B)
\[\left( \frac{a+b}{3},\frac{b+1}{3} \right)\] done
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C)
\[(b,0)\] done
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D)
\[(a-b,a+b)\] done
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question_answer17)
If A (5, 3), B (11, - 5) and P (12, y) are the vertices of a right angled triangle, right angled at P, then y is _______.
A)
4 done
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B)
? 2 done
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C)
? 4 done
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D)
3 done
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question_answer18)
Area of quadrilateral formed by the vertices (- 1, 6), (-3, -9), (5, -8) and (3, 9) is ____ sq.
A)
96 done
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B)
18 done
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C)
50 done
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D)
25 done
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question_answer19)
If P and Q are the points on the line joining A (-2, 5), B (3, 1) such that AP = PQ = QB. then the mid-point of PQ is:
A)
\[\left( \frac{1}{2},3 \right)\] done
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B)
\[\left( -\frac{1}{2},4 \right)\] done
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C)
\[(2,3)\] done
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D)
\[(-1,3)\] done
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question_answer20)
If the centroid of the triangle whose vertices are (2, 4), (3, k), (4, 2) is (k, 3) then k is
A)
4 done
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B)
1 done
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C)
3 done
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D)
2 done
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question_answer21)
The points (-5, 6), (3, 0) and (9, 8) form the vertices of an
A)
Equilateral triangle done
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B)
Isosceles triangle done
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C)
Isosceles right-angled triangle done
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D)
Right-angled triangle done
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question_answer22)
The centre of a circle is C (2, k) .If A (2, 1) and B (5, 2) are two points on its circumference , then the value of k is
A)
6 done
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B)
2 done
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C)
-6 done
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D)
-2 done
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question_answer23)
Find the coordinates of in centre of a triangle PQR whose vertices are P (15, 15); Q (47, 40); R (65, 20) and whose sides are QR = 26.9; RP = 50.2 and PQ = 40.6.
A)
(46, 20) done
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B)
(46, 27) done
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C)
(27, 27) done
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D)
(44, 25) done
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question_answer24)
If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, - 3) and (3, 4) Find the centroid.
A)
\[\left( 3,\frac{2}{3} \right)\] done
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B)
\[\left( 2,\frac{3}{4} \right)\] done
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C)
\[\left( 2,\frac{2}{3} \right)\] done
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D)
None of these done
clear
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question_answer25)
If the coordinates of the midpoint of the sides of a triangle are (1, 2), (0, - 1) and (2, - 1). Find the coordinates of its vertices:
A)
(1, - 4), (3, 2), (-1, 2) done
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B)
(1, 2), (2, 3), (3, - 4) done
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C)
(3, 4), (5, 2), (1, 2) done
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D)
(3, 2), (-1, 2), (1, - 4) done
clear
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question_answer26)
Find (x, y) if (3, 2), (6, 3), (x, y) and (6, 5) are the vertices of a parallelogram:
A)
(5, 6) done
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B)
(6, 5) done
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C)
(9, 6) done
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D)
(9, 5) done
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question_answer27)
Determine the ratio in which \[y-x+2=0\] divides the line joining (3, - 1) and (8, 9):
A)
\[3:5\] done
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B)
\[4:3\] done
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C)
\[2:3\] done
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D)
\[2:5\] done
clear
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question_answer28)
The distance between the point \[(a\,cos\,\theta +b\,sin\,\theta ,\,0)\]and \[(0,\,\,a\,\sin \,\theta -b\,\cos \,\theta )\] is___.
A)
\[{{a}^{2}}+{{b}^{2}}\] done
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B)
\[a+b\] done
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C)
\[\sqrt{{{a}^{2}}-{{b}^{2}}}\] done
clear
D)
\[\sqrt{{{a}^{2}}+{{b}^{2}}}\] done
clear
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question_answer29)
If the coordinates of the points A, B, C and D are (6, 3), (- 3, - 5), (4, - 2) and (a, 3a) respectively and if the ratio of the area of triangles ABC and DBC is \[2:1\], then the value of a is
A)
\[\frac{-9}{2}\] done
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B)
\[\frac{9}{2}\] done
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C)
\[\frac{-23}{36}\] done
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D)
\[\frac{23}{18}\] done
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question_answer30)
The extremities of a diagonal of a parallelogram are the points (3, - 4) and (- 6, 5). If the third vertex is the point (- 2, 1). The coordinate of the fourth vertex is
A)
(1, 0) done
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B)
(-1, 0) done
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C)
(- 1, 1) done
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D)
(1, -1) done
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question_answer31)
The area of triangle formed by the points (p, 2-2p), (1 -p, 2p) and (-4p, 6 -2 p) is 70 units. How many integral values of p are possible?
A)
2 done
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B)
3 done
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C)
4 done
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D)
None of these done
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question_answer32)
Four vertices of a parallelogram taken in order are (- 3, -1), (a, b), (3, 3) and (4, 3). What will be the ratio of a to b?
A)
\[4:1\] done
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B)
\[1:2\] done
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C)
\[1:3\] done
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D)
\[3:1\] done
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question_answer33)
The area of the triangle with vertices at \[(a,b+c,)\text{ (}b,c+a)\] and \[(c,a+b)\] is
A)
\[0\] done
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B)
\[a+b+c\] done
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C)
\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] done
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D)
\[1\] done
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question_answer34)
The points (p - 1, p + 2), (p, p +1), (p + 1, p), are collinear for
A)
\[p=0\] done
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B)
\[p=1\] done
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C)
\[p=1/2\] done
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D)
Any value of p done
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question_answer35)
Find the area of the quadrilateral the coordinates of whose angular points taken in order are (-1, 6), (-3, -9), (5, -8) and (3, 9).
A)
48 done
clear
B)
96 done
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C)
192 done
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D)
72 done
clear
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question_answer36)
Find the third vertex of the triangle whose two vertices are (-3, 1) and (0, -2) and the centroid is the origin.
A)
\[(2,3)\] done
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B)
\[\left( \frac{-4}{3},\frac{14}{3} \right)\] done
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C)
\[(3,1)\] done
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D)
\[(6,4)\] done
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question_answer37)
Points (6, 8), (3, 7), (-2, -2) and (1, -1) are joined to form a quadrilateral. What will this structure be?
A)
Rhombus done
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B)
Parallelogram done
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C)
Square done
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D)
Rectangle done
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question_answer38)
How many squares are possible if two of its vertices are (1, 0) and (2, 0)?
A)
1 done
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B)
2 done
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C)
3 done
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D)
4 done
clear
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question_answer39)
If A (2, 2), B (-4, -4) and C (5, -8) are the vertices of a triangle, then the length of the median through vertex C is ______.
A)
\[\sqrt{65}\,units\] done
clear
B)
\[\sqrt{117}\,units\] done
clear
C)
\[\sqrt{85}\,units\] done
clear
D)
\[\sqrt{113}\,units\] done
clear
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question_answer40)
What is the relation between x and y, if the points (x, y), (1, 2) and (7, 0) are collinear?
A)
\[x-3y+7=0\] done
clear
B)
\[x-3y-7=0\] done
clear
C)
\[x+3y-7=0\] done
clear
D)
\[x+3y+7=0\] done
clear
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