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

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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
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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

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