Question

Point P has the coordinates (−2,−4). Point P is dilated with a center at the origin and a scale factor of 3 to create point P'. What are the coordinates of point P'?

A) (6,12)
B) (1,−1)
C) (−2/3,−4/3)
D) (−6,−12)

Answer 1

Dilation centred at origin

So new coordinates are same like previous

Now scale factor is 3

So P':-

• 3(-2,-4)
• (-6,-12)

Option D

Answer 2

D) (−6, −12)

Explanation:

Dilation: A type of transformation that makes the pre-image larger or smaller without changing its shape.

Center of a dilation: a fixed point about which all points are dilated.

When the center of dilation is the origin (0, 0), simply multiply the coordinates of the points of the pre-image by the scale factor to determine the points of the image after dilation.

Given:

• Point P = (-2, -4)
• Center of dilation = (0, 0)
• Scale factor = 3

Therefore:

⇒ P' = (-2 × 3, -4 × 3)

⇒ P' = (-6, -12)