(C) Given points are $A(-1, 5)$,$B(0, 0)$,and $C(2, 2)$.$D$ is the midpoint of $BC$,so $D = (\frac{0+2}{2}, \frac{0+2}{2}) = (1, 1)$.The slope of line

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(C) Given points are $A(-1, 5)$,$B(0, 0)$,and $C(2, 2)$.$D$ is the midpoint of $BC$,so $D = (\frac{0+2}{2}, \frac{0+2}{2}) = (1, 1)$.The slope of line $AD$ is $m_{AD} = \frac{1-5}{1-(-1)} = \frac{-4}{2} = -2$.The equation of line $AD$ is $y - 5 = -2(x + 1)$,which simplifies to $2x + y - 3 = 0$.The line perpendicular to $AD$ has a slope $m = -\frac{1}{m_{AD}} = \frac{1}{2}$.Since this line passes through $B(0, 0)$,its equation is $y - 0 = \frac{1}{2}(x - 0)$,which simplifies to $x - 2y = 0$.

Class 11 Mathematics Straight Lines Foot of perpendicular, Image of a point and Reflexive properties

Medium

If the coordinates of the points $A, B, C$ are $(-1, 5), (0, 0)$ and $(2, 2)$ respectively and $D$ is the midpoint of $BC$,then the equation of the perpendicular drawn from $B$ to the line $AD$ is

A
$x + 2y = 0$
B
$2x + y = 0$
C
$x - 2y = 0$
D
$2x - y = 0$

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Straight Lines

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Foot of perpendicular, Image of a point and Reflexive properties

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MediumAP EAMCET 2023

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EasyAP EAMCET 2015

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Find the equation of the straight line passing through $(0,0)$ and the foot of the perpendicular from $(2,4)$ onto the line $x+y-1=0$.

EasyAP EAMCET 2022

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$A$ ray of light incident along a line meets another line $7x - y + 1 = 0$ at the point $(0, 1)$ and is then reflected from this point along the line $y + 2x = 1$. Then the equation of the line of incidence of the ray of light is

MediumAP EAMCET 2023

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The equation of the straight line which passes through the point $(a \cos^{3} \theta, a \sin^{3} \theta)$ and is perpendicular to $x \sec \theta + y \operatorname{cosec} \theta = a$ is

MediumKCET 2021

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If the coordinates of the points $A, B, C$ are $(-1, 5), (0, 0)$ and $(2, 2)$ respectively and $D$ is the midpoint of $BC$,then the equation of the perpendicular drawn from $B$ to the line $AD$ is

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If the $y$-intercept of the perpendicular bisector of the line segment joining $P(1, 4)$ and $Q(k, 3)$ is $-4$,then a possible value of $k$ is

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