Question

On a coordinate plane, triangle X prime Y prime Z prime has points (negative 4, 5), (negative 6, negative 1), and (negative 2, negative 1).

Triangle XYZ was dilated using the rule DO,0.25 (x, y) → (0.25x, 0.25y).

The image is shown in the diagram. What are the coordinates of Z of the pre-image?

(–8, –4)
(–8, 2)
(–2, –1)
(–0.25, –0.5)

Answer 1

Answer: a (-8,-4)

Explanation:

Answer 2

(–8, –4)

Explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the reduction or enlargement of the size of an object by a factor.

Given that triangle XYZ was dilated using the rule (x, y) ⇒ (0.25x, 0.25y) to produce triangle X'Y'Z' with points at X'(-4, 5), Y'(-6, -1) and Z'(-2, -1)

Since (x, y) ⇒ (0.25x, 0.25y)

(x, y) ⇒ 0.25(x, y)

4(x, y) ⇒ (x, y)

We can find the points of XYZ by multiplying by 4

hence:

X = 4(-4, 5) = (-16, 20)

Y = 4(-6, -1) = (-24, -4)

Z = 4(-2, -1) = (-8, -4)