Triangle ABC has vertices point A(−2,−2), point B(−4,−3), and point C(−2,−5). Find the coordinates of A′, B′, and C′ after a dilation with a scale factor of 3
and a center point of dilation at the origin.(2 points)
A′= (
)
B′= (
)
C′= (
)
To find the coordinates of A′, B′, and C′ after a dilation with a scale factor of 3 and a center point of dilation at the origin, we can use the formula for dilation:
A′ = (x1 * k, y1 * k)
B′ = (x2 * k, y2 * k)
C′ = (x3 * k, y3 * k)
where (x1, y1) represents the coordinates of point A, (x2, y2) represents the coordinates of point B, (x3, y3) represents the coordinates of point C, and k represents the scale factor.
Given the coordinates of point A(-2, -2), point B(-4, -3), and point C(-2, -5), and a scale factor of 3, we can calculate the coordinates of A′, B′, and C′ as follows:
A′ = (-2 * 3, -2 * 3)
= (-6, -6)
B′ = (-4 * 3, -3 * 3)
= (-12, -9)
C′ = (-2 * 3, -5 * 3)
= (-6, -15)
Therefore, the coordinates of A′ are (-6, -6), B′ are (-12, -9), and C′ are (-6, -15).
To find the coordinates of A', B', and C' after a dilation with a scale factor of 3 and a center point of dilation at the origin, we can use the formula for dilation:
(x', y') = (k * x, k * y)
Where (x, y) are the original coordinates, (x', y') are the coordinates after dilation, and k is the scale factor.
For point A(-2, -2):
A' = (3 * -2, 3 * -2) = (-6, -6)
So, A' is (-6, -6).
For point B(-4, -3):
B' = (3 * -4, 3 * -3) = (-12, -9)
So, B' is (-12, -9).
For point C(-2, -5):
C' = (3 * -2, 3 * -5) = (-6, -15)
So, C' is (-6, -15).
Therefore:
A' = (-6, -6)
B' = (-12, -9)
C' = (-6, -15)