Question

Triangle ABC is graphed on a coordinate grid with vertices at A (-2, -4), B (2, -4) and C (0, 2). Triangle ABC is dilated by a scale factor of x with the origin as the center of dilation to create triangle A’B’C with the vertices A’ (-1, -2), B’(1, -2), C’ (0, 1).

Which rule best represents the dilation that was applied to Triangle ABC to create A’B’C’?

(x, y) (2x, 2y)

(x, y) (0.2x, 0.2y)

(x, y) (12x, 12y)

(x, y) (14x, 14y)

Answer 1

The rule which best represents the dilation that was applied to Triangle ABC to create A’B’C’ will be:

(x, y) → (1/2x, 1/2y)

Explanation:

Given the vertices of a triangle

• A(-2, -4)

• B(2, -4)

• C(0, 2)

After the dilation, the vertices of an image triangle be

• A' (-1, -2)

• B '(1, -2)

• C' (0, 1)

If we closely observe, we can notice that the image triangle vertices A'B'C' are half of the original triangle ABC.

i.e. (x, y) → (1/2x, 1/2y)

verification

A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2)

B(2, -4) → B'(2/2, -4/2) = B'(1, -2)

C(0, 2) → C'(0/2, 2/2) = C'(0, 1)

Thus, it is verified and we conclude that the rule which best represents the dilation that was applied to Triangle ABC to create A’B’C’ will be:

• (x, y) → (1/2x, 1/2y)