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Let A = (6,2) , and let B be the reflection of A over the line y=2x + 5. Find the coordinates of B.

 Feb 28, 2021
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Honestly, I rly like graphing problems :P

 

if it's a reflection, then the line that contains the reflected point and the real point is perpendicular to y=2x+5, so the equation would be y=-1/2x+b, and we can plug in (6,2) for x and y, and we get b=1. now, we can find the intersection, then multiply how much the x coordinate moved and how much the y coordinate moved by 2 and add those to the original point, and voila, we get our answer.

 

intersection: 0=5/2x+4

5/2x=-4

x=-8/5

y=4/5+5/5=9/5

 

so the intersection is (-8/5,9/5). 

the x coordinate moved by -38/5, while the y coordinate moved by 1/5, so we need to move the x coordinate by -76/5, and the y coordinate by 2/5, so the coordinate of B=$\boxed{(-\frac{46}{5},\frac{12}{5})}$

 Feb 28, 2021

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