Question

Which translation rule can be used to prove that triangle r(10,6), s(8,4), t(6,6) and triangle r'(7,4), s'(5,2) t'(3,4)are congruent?

a) (x,y) → (x - 3, y - 2)
b) (x,y) → (x + 3, y + 2)
c) (x,y) → (x - 3, y + 2)
d) (x,y) → (x + 3, y - 2)

Answer 1

a) (x,y) → (x - 3, y - 2)

Explanation:

Comparing the pre-image points, r, s and t, to the image points, r', s' and t', we see that the x-coordinates of the image are all 3 less than the x-coordinates of the image:

10-7 = 3; 8-5 = 3; 6-3 = 3

This means the first part of the translation rule will be x-3.

Now comparing the y-coordinates, we see that the y-coordinates of the image are all 2 less than the y-coordinates of the pre-image:

6-4 = 2; 4-2 = 2; 6-4 = 2

This means the second part of the translation rule will be y-2.

This gives us (x, y)→(x-3, y-2).

Answer 2

a) (x,y) =(x-3, y-2)