Question

Given that the coordinates of the point A is (3,-2). Find the coordinates of the point B such that B is the reflection of A in the line x+y=6.

Find the image of the point P(2,1) under a reflection in the line y=x+2.

Answer 1

let be that the point b is (h,k). Then mid point of B and A should lie on the line (x +y) = 6
hence (h + 3) + (k -2) = 12
also slope of AB should be perp to line's = slope of AB is 1
k + 2 = h - 3

solve both to get h = 9, k = 4

(9,4)

Answer 2

for the other part let image of p be q (h,k)
again same thing (k +1)/2 = (h+2)/2+2
and (h-2) = -(k-1)

solve and get (-1,4)

Answer 3

Ok. But if I use a graph paper, I don't get the same answer as you. I got (8,3) for the first question. Why is that? :O
The second one is right.

Answer 4

hmm .. well check my calculation .. the method is correct .. or check your plotting ...