2. The dashed triangle is a dilation image of the solid triangle. What is the scale factor? (1 point) The coordinates of the solid triangle are A (2,2) B (-2,2) and C (4,-2). A' is (-4,4) B' is (4,4) and C' is (8,-4).
Options are
A. 1/4
B. 1/2
C. 2/3
D. 2
Thank you SO SO SO much in advance! Love you all!
P.S I think it is D. Am I correct?
Thx,
Jen
To find the scale factor, we need to compare the corresponding side lengths of the solid triangle and the dashed triangle.
The distance formula can be used to find the length of a side with two given points. The formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Using this formula, we can find the length of side AB for the solid triangle:
d(AB) = √((-2 - 2)² + (2 - 2)²)
= √((-4)² + 0²)
= √(16)
= 4
Similarly, we can find the length of side A'B' for the dashed triangle:
d(A'B') = √((4 - (-4))² + (4 - 4)²)
= √(8² + 0²)
= √(64)
= 8
The scale factor is then calculated by dividing the length of the corresponding side of the dashed triangle (A'B') by the length of the corresponding side of the solid triangle (AB):
Scale factor = d(A'B') / d(AB)
= 8 / 4
= 2
Therefore, the correct answer is D. 2.
To find the scale factor of a dilation, we need to compare the corresponding side lengths of the original figure and its image. We'll use the distance formula to find the lengths of the sides.
Let's label the sides of the solid triangle and its image. The solid triangle has sides AB, BC, and AC, and the image has sides A'B', B'C', and A'C'.
Using the distance formula:
- For AB: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
- For A'B': distance = sqrt((x2' - x1')^2 + (y2' - y1')^2)
For AB, substituting the coordinates A (2,2) and B (-2,2), we have:
AB = sqrt((-2 - 2)^2 + (2 - 2)^2)
= sqrt((-4)^2 + (0)^2)
= sqrt(16 + 0)
= sqrt(16)
= 4
For A'B', substituting the coordinates A' (-4,4) and B' (4,4), we have:
A'B' = sqrt((4 - (-4))^2 + (4 - 4)^2)
= sqrt((8)^2 + (0)^2)
= sqrt(64 + 0)
= sqrt(64)
= 8
Now, we can compare the lengths of AB and A'B' to find the scale factor.
The scale factor is determined by dividing the length of the image side by the corresponding original side. Using A'B' and AB, we have:
Scale factor = A'B' / AB
= 8 / 4
= 2
Therefore, the scale factor is 2. Thus, the correct option is D.