Triangle ABC has vertices point A(2, 1), point B(−2, 2), and point C(−3,−1). After dilation, triangle A′B′C′ has vertices point A′(4, 2), point B′(−4, 4), and point C′(−6,−2). Determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0, 0 ).(1 point)

Question

The scale factor is
.

Answer 1

To find the scale factor, we can use the formula:

scale factor = |A'B'| / |AB|

Let's calculate the distances:

|A'B'| = √((4-0)^2 + (2-0)^2) = √(16+4) = √20 = 2√5

|AB| = √((2-(-2))^2 + (1-2)^2) = √(4^2 + (-1)^2) = √(16+1) = √17

So, the scale factor is:

scale factor = |A'B'| / |AB| = (2√5) / (√17) = (2√5)√17 / (√17)√17 = (2/√17) * (√85) = 2√(5/17) * (√17)

Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin is 2√(5/17) * (√17).