How to find reflection of a point about a line

Asked by admin @ in Mathematics viewed by 346 People

The point is the reflection of the point (- 7, 5) in the line 5x - 3y = 18 . Find the coordinates of P.

Answered by admin @


Answer:

Hello,

Step-by-step explanation:

slope of the line:

5x-3y=18\\\\y=\dfrac{5x-18}{3} \\\\slope=\dfrac{5}{3} \\\\\\slope\ of\ the\ perpendicular\ line=-\dfrac{3}{5} \\\\\\Equation\ of\ the\ perpendicular\ passing\ through\ (-7,5):\\\\y-5=(x+7)*\dfrac{-3}{5} \ or\ 5y-25=-3x-21 \ or\ 3x+5y=4\\\\\\\\Finding\ intersection\ of the\ line\ and\ the \ perpendicular:\\\\\left \{ \begin{array}{ccc}3x+5y&=&4\\5x-3y&=&15\\\end{array}\right.\\\\\left \{ \begin{array}{ccc}y&=&-1\\x&=&3\\\end{array}\right.\\\\\\

P'=(-7,5)

A=(3,-1)

\overrightarrow{P'A}=(3-(-7),-1-5)=(10,-6)

P=(3,-1)+(10,-6)=(13,-7)


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