Question

Write the coordinates of the imeage of the point (3,8) in the line $x+3y-7=0$.

Answer 1

Let images of the point A(3,8) in the line

$x+3y-7=0$ be $B(h,k)$

Line AB is perpendicular to $x+3y-7=0$

Slope of AB $\left(m_1\right)=\frac{k-8}{h-3}$ $x+3y-7=0$

$3y=-x+7$

$y=-\frac{1}{3}x+7$

$m_2=-\frac{1}{3}$

$m_1{m}_2=-1$

$\left(\frac{k-8}{h-3}\right)\times (-\frac{1}{3})=-1$

$k-8=3(h-3)$

$k-8=3h-9$

$3h-k=1$ ...(1)

M is mid-point of AB, so

$M(\frac{h+3}{2},\frac{k+7}{2})$ is on the line,so.

$\frac{h+3}{2}+3\left(\frac{k+8}{2}\right)-7=0$

$h+3+3k+24-14=0$

$h+3k=-13$ ...(2)

$h=-1,k=-4$ Hence,(-1,-4) is the image of (3,8).