Question

(3, -1) is the image of the point P (-3,5) about the line ax + by + c = 0 find the value of $\frac{-a}{b}$

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Answer 1

The line PQ is perpendicular to L.R is a point on the line L and it is the mid point of P and Q.

To find $\frac{-a}{b}$ , we will first find the equation of L.

We can find one point (R) and the slope of the line L, (L is r to PQ)

1) Finding R

R $\equiv$ $(\frac{-3+3}{0},\frac{5+1}{2})$

$\equiv$ (0,2)

2) Finding slope of PQ

$m_1=\frac{5-(-1)}{-3-3}=-1$

3) Finding slope of L

Let $m_2$ be the slope of L

$m_1{m}_2=-1$

$\Rightarrow$ -1 × $m_2$ = -1

$\Rightarrow$ $m_2=-1$

4) Finding the equation of 2

y - 32 = 1 (x-0)

$\Rightarrow$ x - y + 2 = 0

5) Finding $\frac{-a}{b}$

$\frac{-a}{b}=\frac{-1}{-1}=1$

$\frac{-a}{b}$ is the slope of the line ax + by + c = 0 . We can directly find it after getting the slope of PQ