Question

Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C' has coordinates of (7.2, 3.6). What is the scale factor of the dilation and what are the coordinates of point A'

Answer 1

General Idea:

When we are given a point P(x, y) centered at origin with a scale factor of k, then the dilated point will be given by P' (kx, ky)

Applying the concept:

In the diagram given, the coordinate of C is (6, 3). Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C' has coordinates of (7.2, 3.6).

If C (x, y) centered at origin with a scale factor of k, then the dilated point will be given by C' (kx, ky)

We know $x = 6$ & $kx = 7.2$

Substituting 6 for x in the equation $kx = 7.2$, we get $6k = 7.2$.

Dividing 6 on both sides$\frac{6k}{6}=\frac{7.2}{6}$

Simplifying fractions on both sides$k=1.2$

Point A from the diagram is (-3, 3)

x-coordinate of A' = $kx=1.2 * -3 = -3.6$

y-coordinate of A' = $ky =1.2*3=3.6$

Point A' is given by (-3.6, 3.6)

Conclusion:

Scale factor of dilation is 1.2

The coordinates of point A' is (-3.6, 3.6)

Answer 2

TLDR: The answer is The scale factor is 1.2 and the coordinates of point A' are (–3.6, 3.6).