JEE Main & Advanced Mathematics Straight Line Question Bank

done Foot of perpendicular, Transformation, Pedal points Image of a point Total Questions - 17

• question_answer1)
  The coordinates of the foot of the perpendicular from the point (2, 3) on the line \[y=3x+4\] are given by [MP PET 1984]
  A)
             \[\left( \frac{37}{10},-\frac{1}{10} \right)\]                                done clear
  B)
             \[\left( -\frac{1}{10},\frac{37}{10} \right)\] done clear
  C)
             \[\left( \frac{10}{37},-10 \right)\]    done clear
  D)
             \[\left( \frac{2}{3},-\frac{1}{3} \right)\] done clear
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• question_answer2)
  Coordinates of the foot of the perpendicular drawn from      (0,0) to the line joining \[(a\cos \alpha ,a\sin \alpha )\] and \[(a\cos \beta ,a\sin \beta )\] are  [IIT 1982]
  A)
             \[\left( \frac{a}{2},\frac{b}{2} \right)\] done clear
  B)
             \[\left[ \frac{a}{2}(\cos \alpha +\cos \beta ),\frac{a}{2}(\sin \alpha +\sin \beta ) \right]\] done clear
  C)
             \[\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)\]           done clear
  D)
             None of these done clear
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• question_answer3)
  The coordinates of the foot of the perpendicular from \[({{x}_{1}},{{y}_{1}})\]to the line \[ax+by+c=0\] are      [Dhanbad Engg. 1973]
  A)
             \[\left( \frac{{{b}^{2}}{{x}_{1}}-ab{{y}_{1}}-ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}-ab{{x}_{1}}-bc}{{{a}^{2}}+{{b}^{2}}} \right)\] done clear
  B)
             \[\left( \frac{{{b}^{2}}{{x}_{1}}+ab{{y}_{1}}+ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}+ab{{x}_{1}}+bc}{{{a}^{2}}+{{b}^{2}}} \right)\] done clear
  C)
             \[\left( \frac{a{{x}_{1}}+b{{y}_{1}}+ab}{a+b},\frac{a{{x}_{1}}-b{{y}_{1}}-ab}{a+b} \right)\] done clear
  D)
             None of these done clear
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• question_answer4)
  The foot of the coordinates drawn from (2, 4) to the line \[x+y=1\] is                                                [Roorkee 1995]
  A)
             \[\left( \frac{1}{3},\frac{3}{2} \right)\]                                        done clear
  B)
             \[\left( -\frac{1}{2},\frac{3}{2} \right)\] done clear
  C)
             \[\left( \frac{4}{3},\frac{1}{2} \right)\]                                        done clear
  D)
             \[\left( \frac{3}{4},\,\,-\frac{1}{2} \right)\] done clear
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• question_answer5)
  The co-ordinates of the foot of perpendicular from the point (2, 3) on the line \[x+y-11=0\]are       [MP PET 1986]
  A)
             \[(-6,\,5)\]                                 done clear
  B)
             \[(5,\,6)\] done clear
  C)
             \[(-5,\,6)\]                                 done clear
  D)
             \[(6,\,5)\] done clear
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• question_answer6)
  The line \[2x+3y=12\]meets the x-axis at A and y-axis at B. The line through (5, 5) perpendicular to \[AB\]meets the x- axis , y axis and the \[AB\] at C, D and E respectively. If O is the origin of coordinates, then the area of \[OCEB\]is  [IIT 1976]
  A)
             \[23\] sq. units                          done clear
  B)
             \[\frac{23}{2}sq.\]units done clear
  C)
             \[\frac{23}{3}sq.\]units             done clear
  D)
             None of these done clear
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• question_answer7)
  If A and B are two points on the line \[3x+4y+15=0\]such that \[OA=OB=9\]units, then the area of the triangle \[OAB\] is 
  A)
             18 sq. units                                done clear
  B)
             \[18\sqrt{2}sq.\]units done clear
  C)
             18/\[\sqrt{2}\]sq. units             done clear
  D)
             None of these done clear
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• question_answer8)
  One vertex of the equilateral triangle with centroid at the origin and one side as \[x+y-2=0\]is
  A)
             \[(-1,-1)\]                                   done clear
  B)
             \[(2,2)\] done clear
  C)
             \[(-2,-2)\]                                   done clear
  D)
             None of these done clear
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• question_answer9)
  The point (4, 1)undergoes the following two successive transformation (i)        Reflection about the line \[y=x\] (ii)       Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are [MNR 1987; UPSEAT 2000]
  A)
             (4, 3)                                          done clear
  B)
             (3, 4) done clear
  C)
             (1, 4)                                          done clear
  D)
             \[\left( \frac{7}{2},\frac{7}{2} \right)\] done clear
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• question_answer10)
  Line L has intercepts a and b on the co-ordinate axes. When the axes are rotated through a given angle keeping the origin fixed, the same line L has intercepts p and q, then   [IIT 1990; Kurukshetra CEE 1998]
  A)
             \[{{a}^{2}}+{{b}^{2}}={{p}^{2}}+{{q}^{2}}\]                                   done clear
  B)
             \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}+\frac{1}{{{q}^{2}}}\] done clear
  C)
             \[{{a}^{2}}+{{p}^{2}}={{b}^{2}}+{{q}^{2}}\]                                   done clear
  D)
             \[\frac{1}{{{a}^{2}}}+\frac{1}{{{p}^{2}}}=\frac{1}{{{b}^{2}}}+\frac{1}{{{q}^{2}}}\] done clear
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• question_answer11)
  Let L be the line \[2x+y=2\]. If the axes are rotated by \[{{45}^{o}}\], then the intercepts made by the line L on the new axes are respectively [Roorkee Qualifying 1998]
  A)
             \[\sqrt{2}\]and 1                       done clear
  B)
             1 and \[\sqrt{2}\] done clear
  C)
             \[2\sqrt{2}\]and  \[2\sqrt{2}/3\]      done clear
  D)
             \[2\sqrt{2}/3\]and \[2\sqrt{2}\] done clear
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• question_answer12)
  The pedal points of a perpendicular drawn from origin on the line \[3x+4y-5=0\],  is                                        [RPET 1990]
  A)
             \[\left( \frac{3}{5},2 \right)\]   done clear
  B)
             \[\left( \frac{3}{5},\frac{4}{5} \right)\] done clear
  C)
             \[\left( -\frac{3}{5},-\frac{4}{5} \right)\]                                     done clear
  D)
             \[\left( \frac{30}{17},\frac{19}{17} \right)\] done clear
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• question_answer13)
  The image of a point \[A(3,\,8)\]in the line \[x+3y-7=0\], is  [RPET 1991]
  A)
             \[(-1,-4)\]                                   done clear
  B)
             \[(-3\,,\,\,-8)\] done clear
  C)
             \[(1,-4)\]                                    done clear
  D)
             \[(3,\,8)\] done clear
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• question_answer14)
  The reflection of the point (4, -13) in the line \[5x+y+6=0\] is                                                             [EAMCET 1994]
  A)
  \[(-1,-14)\]                                 done clear
  B)
  (3 ,4) done clear
  C)
  (1, 2)                                          done clear
  D)
  (- 4, 13) done clear
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• question_answer15)
  If (- 2, 6) is the image of the point (4, 2) with respect to line L = 0, then L =                                      [EAMCET 2002]
  A)
             3x ? 2y + 5                                  done clear
  B)
             3x ? 2y + 10 done clear
  C)
             2x + 3y ? 5                                  done clear
  D)
             6x ? 4y ? 7 done clear
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• question_answer16)
  A straight line passes through a fixed point \[(h,k)\]. The locus of the foot of perpendicular on it drawn from the origin is
  A)
             \[{{x}^{2}}+{{y}^{2}}-hx-ky=0\]  done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}+hx+ky=0\] done clear
  C)
             \[3{{x}^{2}}+3{{y}^{2}}+hx-ky=0\]     done clear
  D)
             None of these done clear
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• question_answer17)
  If for a variable line \[\frac{x}{a}+\frac{y}{b}=1\], the condition \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}}\] (c is a constant) is satisfied, then locus of foot of perpendicular drawn from origin to the line is  [RPET 1999]
  A)
             \[{{x}^{2}}+{{y}^{2}}={{c}^{2}}/2\]    done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}=2{{c}^{2}}\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}={{c}^{2}}\]        done clear
  D)
             \[{{x}^{2}}-{{y}^{2}}={{c}^{2}}\] done clear
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