Rectangle ABCD has vertices point A(−5, 1), point B(−2, 1), point C(−2, 6), and point D(−5, 6). Find the coordinates of A′, B′, C′, and D′ after a dilation with a scale factor of 3 and a center point of dilation at the origin.
To find the coordinates of the new points A′, B′, C′, and D′ after a dilation with a scale factor of 3 and a center point of dilation at the origin, we need to multiply the coordinates of each of the original points by the scale factor.
Original coordinates:
A(−5, 1)
B(−2, 1)
C(−2, 6)
D(−5, 6)
Coordinates after dilation:
A′ = 3 * A = 3 * (−5, 1) = (−15, 3)
B′ = 3 * B = 3 * (−2, 1) = (−6, 3)
C′ = 3 * C = 3 * (−2, 6) = (−6, 18)
D′ = 3 * D = 3 * (−5, 6) = (−15, 18)
Therefore, the coordinates of the new points A′, B′, C′, and D′ after a dilation with a scale factor of 3 and a center point of dilation at the origin are:
A′(−15, 3)
B′(−6, 3)
C′(−6, 18)
D′(−15, 18)