Question

The dashed triangle is the image of the solid triangle. The center of dilation is (6, 6) .

What is the scale factor used to create the dilation?

Enter your answer as an integer or decimal in the box.

Answer 1

It has to be negitive because it is in BETWEEN the two

Answer 2

Scale factor = -0.2

Explanation:

In the picture attached,

Big (with solid lines) triangle has been dilated to form a new (small in dashed lines).Center of dilation is (6, 6).

Solid line of the bigger triangle has the vertices as (-9, 6) and (6, 6)

So the measure of this leg =
`\sqrt{(6-6)^(2)+(-9-6)^(2)}`

l = 15

corresponding side of the dashed triangle has the vertices (6, 6) and (9, 6)

Measure of this side =
`\sqrt{(6-6)^(2)+(9-6)^(2)}`

l' =
`\sqrt{(9-6)^(2)}`

l' = 3

Scale factor =
`(3)/(15)`

= 0.2

Since the bigger triangle has been inverted so the sign of the scale factor will be negative.

Therefore, the scale factor by which the bigger triangle has been dilated is -0.2