Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 1/3, centered at the origin where the endpoints are A(−6,3) and B(−12,9).
A′(−18,9) and B′(−36,27)
A′(−6,3) and B′(−4,3)
A′(−2,1) and B′(−12,9)
A′(−2,1) and B′(−4,3)
Line AB contains point A(−4, 1) and point B (−1, 3) . Find the coordinates of A′ and B′ after a dilation with a scale factor of 2 with a center point of dilation at the origin.
A′ (−8, 2) and B′ (2, −6)
A′ (8, −2) and B′ (2, −6)
A′ (−5, −2) and B′ (−2, 6)
A′ (−8, 2) and B′ (−2, 6)
To dilate a line segment with a scale factor of 2 centered at the origin, we multiply the coordinates of each endpoint by the scale factor.
For point A (-4,1):
Coordinates of A' = (-4 * 2, 1 * 2) = (-8, 2)
For point B (-1,3):
Coordinates of B' = (-1 * 2, 3 * 2) = (-2, 6)
Therefore, the correct answer is:
A′(-8,2) and B′(-2,6)
To dilate a line segment with a scale factor of 1/3 centered at the origin, we multiply the coordinates of each endpoint by the scale factor.
For point A (-6,3):
Coordinates of A' = (-6 * 1/3, 3 * 1/3) = (-18/3, 3/3) = (-6, 1)
For point B (-12,9):
Coordinates of B' = (-12 * 1/3, 9 * 1/3) = (-36/3, 9/3) = (-12, 3)
Therefore, the correct answer is:
A′(-6,1) and B′(-12,3)