Question

You can transform AIK to AIJ'K' by translating it and then performing a dilation centered at the origin. So, AIK~ AIJK. Find the translation rule and the scale factor of the dilation.

Answer 1

The translation rule is (x, y) → (x + 2, y + 4) and the scale factor of the dilation is 2.

We find the translation rule by finding the vector that translates point A in triangle AIK to point A' in triangle AIJK'.

Translation vector = (A'x - Ax, A'y - Ay) = (2, 4)

Therefore, the translation rule is:

(x, y) → (x + 2, y + 4)

The scale factor is found by dividing the length of a corresponding side in triangle AIJK' by the length of the corresponding side in triangle AIK.

Scale factor = AIJK' / AIK

= (2 + 2) / 2

= 2

The scale factor of the dilation is 2.