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)

Answer 1

To find the scale factor, we can compare the distance between two corresponding vertices of the original and dilated triangle.

Distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)

For example, let's compare the distance between A and A':

d(A, A') = √((4 - 2)^2 + (2 - 1)^2)
= √(2^2 + 1^2)
= √(4 + 1)
= √5

Similarly, we can find the distances between B and B', and C and C':

d(B, B') = √((-4 - (-2))^2 + (4 - 2)^2)
= √((-2)^2 + 2^2)
= √(4 + 4)
= √8 = 2√2

d(C, C') = √((-6 - (-3))^2 + (-2 - (-1))^2)
= √((-3)^2 + (-1)^2)
= √(9 + 1)
= √10

We need to find the scale factor that multiplies the original distances to get the dilated distances:

scale factor = d(A, A') / d(A, A') = √5 / √5 = 1

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

Answer 2

thats wrong

Answer 3

Apologies for the mistake. Let's correct it.

To find the scale factor, we can compare the lengths of two corresponding sides of the original and dilated triangle.

Let's compare the lengths of AB and A'B':

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

Length of A'B' = √((-4 - 4)^2 + (4 - 2)^2)
= √((-8)^2 + 2^2)
= √(64 + 4)
= √68
= 2√17

To find the scale factor, we divide the length of A'B' by the length of AB:

scale factor = Length of A'B' / Length of AB
= (2√17) / √17
= 2

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