I'm not sure if I understood this correctly:

Question

Asked to reflect the point P = (4,0) across the mirror line y = 2x, Aubrey reasoned this way: First mark the point A = (1, 2) on the line, then use the vector [−3, 2] from P to A to reach from A to P ′ = (−2, 4), which is the requested image. Does this make sense to you? Explain.

I feel like this is wrong because [-3, 2] is not perpendicular to the line y=2x. I feel like it should be a vector with a slope of -1/2.

Answer 1

You are correct! The vector <-3, 2> is not perpendicular to the line y= 2x, and therefore is not perpendicular to the line of reflection. You are also correct that the slope to use would be -1/2.

Are you good finding the correct vector, point A, and P'?

Answer 2

You are correct! Look at a diagram.