Let P = (5,1) , and let Q be the reflection of P over the line y=1/2x + 2. Find the coordinates of Q.

waffles
Nov 10, 2017

#1**+2 **

Here's one way to do this

The line perpendicular to the given line will have the equation

y = -2(x - 5) + 1

And we can find the intersection of these lines thusly:

-2 (x - 5) + 1 = (1/2)x + 1

-4x + 20 = x + 2

5x = 18

x = 18/5 and y = (1/2)(18/5) + 2 = 38/10 (18/5, 19/5) ⇒ (3.6, 3.8)

So.......from (5,1) we went back on x by [ 5 - 3.6 ] = 1.4 and up on y by [3.8 - 1] = 2.8 to get from (5,1) to (3.6, 3.8)

So.....from the interesection point of the two lines, we need to do the same thing to determine "Q"

So we have ( 3.6 - 1.4 , 3.8 + 2.8) ⇒ ( 2.2, 6.6) = "Q"

Here's a graph showing this : https://www.desmos.com/calculator/zctunpdnrj

CPhill
Nov 11, 2017