Question
Triangle ABC' has vertices point A (-2, 4), point B (-6,8), and point C' (-2, 4). After dilation, triangle A' B'C" has vertices point A' (-1, 2), point B' (-3, 4), and point C" (-1, 2). Determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0, 0). (1 point)
0-2
02
0-
0-2
02
0-
Answers
Answered by
GPT 3.5
To determine the scale factor of the dilation, we can compare the corresponding side lengths of the two triangles.
First, let's find the length of side AB in triangle ABC.
Using the distance formula:
AB = √[(-6 - (-2))^2 + (8 - 4)^2]
= √[(-4)^2 + (4)^2]
= √[16 + 16]
= √32
= 4√2
Next, let's find the length of side A'B' in triangle A'B'C".
A'B' = √[(-3 - (-1))^2 + (4 - 2)^2]
= √[(-2)^2 + (2)^2]
= √[4 + 4]
= √8
= 2√2
The scale factor is the ratio of the corresponding side lengths:
Scale factor = A'B' / AB
= (2√2) / (4√2)
= (2/4)
= 1/2
Therefore, the scale factor for the dilation is 1/2.
First, let's find the length of side AB in triangle ABC.
Using the distance formula:
AB = √[(-6 - (-2))^2 + (8 - 4)^2]
= √[(-4)^2 + (4)^2]
= √[16 + 16]
= √32
= 4√2
Next, let's find the length of side A'B' in triangle A'B'C".
A'B' = √[(-3 - (-1))^2 + (4 - 2)^2]
= √[(-2)^2 + (2)^2]
= √[4 + 4]
= √8
= 2√2
The scale factor is the ratio of the corresponding side lengths:
Scale factor = A'B' / AB
= (2√2) / (4√2)
= (2/4)
= 1/2
Therefore, the scale factor for the dilation is 1/2.