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)

Responses

12
Start Fraction 1 over 2 End Fraction

2
2

−12

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the scale factor of the dilation, we can compare the distances between the original and dilated vertices.

Let's start with the distance between points A and B in the original triangle ABC:
AB = √((-6 - (-2))^2 + (8 - 4)^2)
AB = √(16 + 16)
AB = √32

Now, let's find the distance between points A' and B' in the dilated triangle A'B'C':
A'B' = √((-3 - (-1))^2 + (4 - 2)^2)
A'B' = √(4 + 4)
A'B' = √8

The scale factor, denoted by k, can be found by dividing the distance in the dilated triangle by the distance in the original triangle:
k = A'B' / AB
k = √8 / √32
k = √(8/32)
k = √(1/4)
k = 1/2

Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin is 1/2.