I need help......

Question

Describe a transformation that carries the triangle with vertices R = (1, 2), P = (6, 7), and Q = (10,5) onto the triangle with vertices K = (0,0), L = (7,−1), and M = (9,3). Where does your transformation send (a) (4, 5)? (b) (7, 5)?

Answer 1

this way works,

translate (move each point) entire triangle x-1,,,y-2

flip the triangle over the base line formed by points (0,0) and (9,3)

so only the third vertex is moved

the flip is over line y=(1/3)x

for point (4,5),,,,translate to (3,3)

flip over line y=(1/3)x

[my method is to find intersection of y=(1/3)x and -3=(y-3)/(x-3)

and then use symmetry to find point after flip].

point of intersection is (3.6,1.2)

point (3,3) after flip is (4.2,-.6)

try for point (7,5)

Answer 2

Reflect over x-axis, then slide using (x, y) → (x - 1, (y + 2)