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.(1 point)
Responses
A′ (−8, 2)
and B′ (2, −6)
upper A prime left parenthesis negative 8 comma 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis
A′ (−8, 2)
and B′ (−2, 6)
upper a prime left parenthesis negative 8 comma 2 right parenthesis and upper b prime left parenthesis negative 2 comma 6 right parenthesis
A′ (8, −2)
and B′ (2, −6)
upper A prime left parenthesis 8 comma negative 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis
A′ (−5, −2)
and B′ (−2, 6)
None of the responses are correct.
To 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, you need to multiply the x and y coordinates of each point by the scale factor.
For point A(-4, 1):
x coordinate of A' = -4 * 2 = -8
y coordinate of A' = 1 * 2 = 2
So, A' has coordinates (-8, 2).
For point B(-1, 3):
x coordinate of B' = -1 * 2 = -2
y coordinate of B' = 3 * 2 = 6
So, B' has coordinates (-2, 6).
Correct answer:
A' (-8, 2) and B' (-2, 6)