-
question_answer1)
The coordinates of a point are (0, 1) and the ordinate of another point is - 3. If the distance between the two points is 5, then the abscissa of another point is
A)
3 done
clear
B)
- 3 done
clear
C)
\[\pm 3\] done
clear
D)
1 done
clear
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question_answer2)
One of the vertices of a square is origin and adjacent sides of the square are coincident with positive axes. If side is 5 then which will not be its one of the vertex
A)
(0, 5) done
clear
B)
(5, 0) done
clear
C)
(- 5, - 5) done
clear
D)
(0, 0) done
clear
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question_answer3)
The common property of points lying on x-axis, is [MP PET 1988]
A)
\[x=0\] done
clear
B)
\[y=0\] done
clear
C)
\[a=0,\,y=0\] done
clear
D)
\[y=0,b=0\] done
clear
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question_answer4)
If the distance between the points \[(a,2)\]and \[(3,4)\]be 8, then \[a=\] [MNR 1978]
A)
\[2+3\sqrt{15}\] done
clear
B)
\[2-3\sqrt{15}\] done
clear
C)
\[2\pm 3\sqrt{15}\] done
clear
D)
\[3\pm 2\sqrt{15}\] done
clear
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question_answer5)
The point whose abscissa is equal to its ordinate and which is equidistant from the points (1,0) and (0,3) is
A)
(1, 1) done
clear
B)
(2, 2) done
clear
C)
(3, 3) done
clear
D)
(4, 4) done
clear
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question_answer6)
If the points \[A(6,-1),\ B\text{ }(1,\,3)\] and \[C(x,\,8)\]be such that \[AB=BC,\]then \[x=\]
A)
- 3, 5 done
clear
B)
3, - 5 done
clear
C)
- 3, - 5 done
clear
D)
3, 5 done
clear
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question_answer7)
The distance between the points \[(am_{1}^{2},\,2a{{m}_{1}})\] and \[(am_{2}^{2},\,2a{{m}_{2}})\] is
A)
\[a({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}+4}\] done
clear
B)
\[({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}+4}\] done
clear
C)
\[a({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}-4}\] done
clear
D)
\[({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}-4}\] done
clear
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question_answer8)
If the point (x, y) be equidistant from the points \[(a+b,\,b-a)\]and \[(a-b,\,a+b),\]then [MP PET 1983, 94]
A)
\[ax+by=0\] done
clear
B)
\[ax-by=0\] done
clear
C)
\[bx+ay=0\] done
clear
D)
\[bx-ay=0\] done
clear
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question_answer9)
If the points (0, 0), \[(2,\,2\sqrt{3})\] and (a, b) be the vertices of an equilateral triangle, then \[(a,\,b)=\]
A)
(0, - 4) done
clear
B)
(0, 4) done
clear
C)
(4, 0) done
clear
D)
(- 4, 0) done
clear
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question_answer10)
The distance between the points \[(a\cos \alpha ,\,a\sin \alpha )\] and \[(a\cos \beta ,a\sin \beta )\]is
A)
\[a\cos \frac{\alpha -\beta }{2}\] done
clear
B)
\[2a\cos \frac{\alpha -\beta }{2}\] done
clear
C)
\[a\sin \frac{\alpha -\beta }{2}\] done
clear
D)
\[2a\sin \frac{\alpha -\beta }{2}\] done
clear
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question_answer11)
A point equidistant from the points (2, 0) and (0, 2) is
A)
(1, 4) done
clear
B)
(2, 1) done
clear
C)
(1, 2) done
clear
D)
(2, 2) done
clear
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question_answer12)
The point on y-axis equidistant from the points (3, 2) and (-1, 3) is
A)
(0, -3) done
clear
B)
(0, -3/2) done
clear
C)
(0, 3/2) done
clear
D)
(0, 3) done
clear
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question_answer13)
If a vertex of an equilateral triangle is on origin and second vertex is (4, 0), then its third vertex is
A)
\[(2,\,\pm \sqrt{3})\] done
clear
B)
\[(3,\,\pm \sqrt{2})\] done
clear
C)
\[(2,\,\pm 2\sqrt{3})\] done
clear
D)
\[(3,\,\pm 2\sqrt{2})\] done
clear
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question_answer14)
If the coordinates of vertices of \[\Delta OAB\] are (0,0) \[(\cos \alpha ,\,\sin \alpha )\] and \[(-\sin \alpha ,\,\cos \alpha )\] respectively, then \[O{{A}^{2}}+O{{B}^{2}}=\]
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
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question_answer15)
The length of altitude through A of the triangle ABC, where \[A\equiv (-3,\,0);\,B\equiv (4,\,-1);\,C\equiv (5,\,2),\] is [Karnataka CET 2001]
A)
\[\frac{2}{\sqrt{10}}\] done
clear
B)
\[\frac{4}{\sqrt{10}}\] done
clear
C)
\[\frac{11}{\sqrt{10}}\] done
clear
D)
\[\frac{22}{\sqrt{10}}\] done
clear
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question_answer16)
The distance of the point \[(b\cos \theta ,\,b\sin \theta )\]from origin is [MP PET 1984]
A)
\[b\cot \theta \] done
clear
B)
\[b\] done
clear
C)
\[b\tan \theta \] done
clear
D)
\[b\sqrt{2}\] done
clear
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question_answer17)
The distance of the middle point of the line joining the points \[(a\sin \theta ,0)\]and \[(0,a\cos \theta )\]from the origin is [MP PET 1999]
A)
\[\frac{a}{2}\] done
clear
B)
\[\frac{1}{2}a(\sin \theta +\cos \theta )\] done
clear
C)
\[a(\sin \theta +\cos \theta )\] done
clear
D)
\[a\] done
clear
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question_answer18)
If the points (1,1), (-1, -1) and \[(-\sqrt{3},k)\]are vertices of an equilateral triangle then the value of k will be
A)
1 done
clear
B)
-1 done
clear
C)
\[\sqrt{3}\] done
clear
D)
\[-\sqrt{3}\] done
clear
View Solution play_arrow
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question_answer19)
The points P is equidistant from A(1,3), B (-3,5) and C(5,-1). Then PA = [EAMCET 2003]
A)
5 done
clear
B)
\[5\sqrt{5}\] done
clear
C)
25 done
clear
D)
\[5\sqrt{10}\] done
clear
View Solution play_arrow
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question_answer20)
The distance between the points (7, 5) and (3, 2) is equal to [Pb. CET 2002]
A)
2 units done
clear
B)
3 units done
clear
C)
4 units done
clear
D)
5 units done
clear
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question_answer21)
If the point dividing internally the line segment joining the points (a, b) and (5, 7) in the ratio 2 : 1 be (4, 6), then
A)
\[a=1,\,b=2\] done
clear
B)
\[a=2,\,b=-4\] done
clear
C)
\[a=2,\,b=4\] done
clear
D)
\[a=-2,\,b=4\] done
clear
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question_answer22)
If the middle point of the line segment joining the points (5, a) and (b,7) be (3,5), then (a, b) =
A)
(3, 1) done
clear
B)
(1, 3) done
clear
C)
(-2,-2) done
clear
D)
(-3, -1) done
clear
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question_answer23)
The ratio in which x-axis divides the join of the points (2, -3) and (5, 6) is
A)
2 : 1 done
clear
B)
1: 2 done
clear
C)
2 : -1 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer24)
The point which divides externally the line joining the points \[(a+b,\,a-b)\] and \[(a-b,a+b)\] in the ratio \[a:b\], is
A)
\[\left( \frac{{{a}^{2}}-2ab-{{b}^{2}}}{a-b},\frac{{{a}^{2}}+{{b}^{2}}}{a-b} \right)\] done
clear
B)
\[\left( \frac{{{a}^{2}}-2ab-{{b}^{2}}}{a-b},\frac{{{a}^{2}}-{{b}^{2}}}{a-b} \right)\] done
clear
C)
\[\left( \frac{{{a}^{2}}-2ab+{{b}^{2}}}{a-b},\frac{{{a}^{2}}+{{b}^{2}}}{a-b} \right)\] done
clear
D)
None of these done
clear
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question_answer25)
The coordinates of the points A, B, C are \[({{x}_{1}},{{y}_{1}})\], \[({{x}_{2}},{{y}_{2}})\], \[({{x}_{3}},\,{{y}_{3}})\] and D divides the line AB in the ratio l : k. If P divides the line DC in the ratio m : k + l, then the coordinates of P are
A)
\[\left( \frac{k{{x}_{1}}+l{{x}_{2}}+m{{x}_{3}}}{k+l+m},\,\frac{k{{y}_{1}}+l{{y}_{2}}+m{{y}_{3}}}{k+l+m} \right)\] done
clear
B)
\[\left( \frac{l{{x}_{1}}+m{{x}_{2}}+k{{x}_{3}}}{l+m+k},\,\frac{l{{y}_{1}}+m{{y}_{2}}+k{{y}_{3}}}{l+m+k} \right)\] done
clear
C)
\[\left( \frac{m{{x}_{1}}+k{{x}_{2}}+l{{x}_{3}}}{m+k+l},\,\frac{m{{y}_{1}}+k{{y}_{2}}+l{{y}_{3}}}{m+k+l} \right)\] done
clear
D)
None of these done
clear
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question_answer26)
The points which trisect the line segment joining the points (0, 0) and (9, 12) are [RPET 1986]
A)
(3, 4), (6, 8) done
clear
B)
(4, 3), (6, 8) done
clear
C)
(4, 3), (8, 6) done
clear
D)
(3, 4), (8, 6) done
clear
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question_answer27)
The line \[x+y=4\] divides the line joining the points (-1, 1) and (5, 7) in the ratio [IIT 1965; UPSEAT 1999]
A)
2 : 1 done
clear
B)
1 : 2 done
clear
C)
1 : 2 externally done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer28)
If the point (x, - 1), (3, y), (- 2, 3) and (- 3, - 2) be the vertices of a parallelogram, then
A)
\[x=2,\,y=4\] done
clear
B)
\[x=1,\,y=2\] done
clear
C)
\[x=4,\,y=2\] done
clear
D)
None of these done
clear
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question_answer29)
The mid-points of sides of a triangle are (2, 1), (-1, -3) and (4,5). Then the coordinates of its vertices are
A)
\[(7,\,9),\,(-3,\,-7),\,(1,\,1)\] done
clear
B)
\[(-3,\,-7),\,(1,\,1),\,(2,\,3)\] done
clear
C)
\[(1,\,1),\,(2,\,3),\,(-5,\,8),\] done
clear
D)
None of these done
clear
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question_answer30)
Point \[\left( \frac{1}{2},\,\frac{-13}{4} \right)\]divides the line joining the points \[(3,-5)\]and \[(-7,2)\] in the ratio of
A)
1 : 3 internally done
clear
B)
3 : 1internally done
clear
C)
1 : 3 externally done
clear
D)
3 : 1externally done
clear
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question_answer31)
The coordinates of the join of trisection of the points (-2, 3), (3, -1) nearer to (-2, 3), is
A)
\[\left( -\frac{1}{3},\,\frac{5}{3} \right)\] done
clear
B)
\[\left( \frac{4}{3},\frac{1}{3} \right)\] done
clear
C)
\[\left( -\frac{3}{4},\,2 \right)\] done
clear
D)
\[\left( \frac{1}{3},\,\frac{5}{3} \right)\] done
clear
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question_answer32)
If the vertices of a triangle are \[A(1,4),\,B(3,0)\]and \[C(2,1),\]then the length of the median passing through C is [RPET 1995]
A)
1 done
clear
B)
2 done
clear
C)
\[\sqrt{2}\] done
clear
D)
\[\sqrt{3}\] done
clear
View Solution play_arrow
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question_answer33)
Three vertices of a parallelogram taken in order are \[(-1,\,-6)\], \[(2,\,-5)\] and \[(7,\,2)\]. The fourth vertex is [Kerala (Engg.) 2002]
A)
(1, 4) done
clear
B)
(4, 1) done
clear
C)
(1, 1) done
clear
D)
(4, 4) done
clear
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question_answer34)
P and Q are points on the line joining A (-2, 5) and B (3, 1) such that AP = PQ = QB. Then the mid-point of PQ is
A)
\[\left( \frac{1}{2},\,3 \right)\] done
clear
B)
\[\left( -\frac{1}{2},\,4 \right)\] done
clear
C)
\[(2,\,3)\] done
clear
D)
\[(1,\,4)\] done
clear
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question_answer35)
The points of trisection of the line segment joining the points (3, -2) and (-3, -4) are
A)
\[\left( \frac{3}{2},-\frac{5}{2} \right)\,,\left( -\frac{3}{2},-\frac{13}{4} \right)\] done
clear
B)
\[\left( -\frac{3}{2},\frac{5}{2} \right)\,,\left( \frac{3}{2},\frac{13}{4} \right)\] done
clear
C)
\[\left( 1,-\frac{8}{3} \right)\,,\left( -1,-\frac{10}{3} \right)\] done
clear
D)
None of these done
clear
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question_answer36)
The coordinates of the point dividing internally the lines joining the points (4, -2) and (8, 6) in the ratio 7 : 5 will be [AMU 1979; MP PET 1984]
A)
\[(16,\,18)\] done
clear
B)
\[(18,\,16)\] done
clear
C)
\[\left( \frac{19}{3},\,\frac{8}{3} \right)\] done
clear
D)
\[\left( \frac{8}{3},\frac{19}{3} \right)\] done
clear
View Solution play_arrow
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question_answer37)
In what ratio does the y-axis divide the join of \[(-3,\,-4)\]and \[(1,-2)\] [RPET 1995]
A)
1 : 3 done
clear
B)
2 : 3 done
clear
C)
3 : 1 done
clear
D)
None of these done
clear
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question_answer38)
If the three vertices of a rectangle taken in order are the points (2, -2), (8, 4) and (5, 7). The coordinates of the fourth vertex is [CEE 1993]
A)
(1, 1) done
clear
B)
(1, -1) done
clear
C)
(-1, 1) done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer39)
The line joining points (2, -3) and (-5,6) is divided by y-axis in the ratio [MP PET 1999]
A)
2 : 5 done
clear
B)
2 : 3 done
clear
C)
3 : 5 done
clear
D)
1 : 2 done
clear
View Solution play_arrow
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question_answer40)
If P (1,2), Q(4,6) R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then [IIT 1998]
A)
\[a=2,\,b=4\] done
clear
B)
\[a=3,\,b=4\] done
clear
C)
\[a=2,\,b=3\] done
clear
D)
\[a=3,\,b=5\] done
clear
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question_answer41)
The extremities of a diagonal of a parallelogram are the points \[(3,-4)\]and \[(-6,5)\]. If third vertex is \[(-2,1)\], then fourth vertex is [RPET 1987]
A)
\[(1,0)\] done
clear
B)
\[(-1,0)\] done
clear
C)
\[(1,\text{ }1)\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer42)
(0, -1) and (0, 3) are two opposite vertices of a square. The other two vertices are [Karnataka CET 2005]
A)
(0, 1), (0, -3) done
clear
B)
(3, -1) (0, 0) done
clear
C)
(2, 1), (-2, 1) done
clear
D)
(2, 2), (1, 1) done
clear
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question_answer43)
If \[A(3,\,5),B(-5,\,-4),C(7,\,10)\] are the vertices of a parallelogram, taken in the order, then the co-ordinates of the fourth vertex are [Kerala (Engg.) 2005]
A)
(10, 19) done
clear
B)
(15, 10) done
clear
C)
(19, 10) done
clear
D)
(19, 15) done
clear
E)
(e) (15, 19) done
clear
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question_answer44)
If the point (a, a) are placed in between the lines \[|x+y|=4\], then [AMU 2005]
A)
| a| = 2 done
clear
B)
\[|a|\,=3\] done
clear
C)
| a| < 2 done
clear
D)
| a| < 3 done
clear
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