To determine the scale factor, we can compare the lengths of corresponding sides of the original triangle ABC and the dilated triangle A'B'C'.
Let's start with side AB. The length of AB is calculated using the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(-2 - 2)^2 + (2 - 1)^2]
= √[(-4)^2 + (1)^2]
= √(16 + 1)
= √17
The length of A'B' can be calculated in the same way:
A'B' = √[(x2' - x1')^2 + (y2' - y1')^2]
= √[(-4 - 4)^2 + (4 - 2)^2]
= √[(-8)^2 + (2)^2]
= √(64 + 4)
= √68
= 2√17
To find the scale factor, we can divide the length of A'B' by the length of AB:
Scale factor = A'B' / AB
= (2√17) / √17
= 2
Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0, 0) is 2.
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)
The scale factor is ____
1 answer