Line AB contains point A(1, 2) and point B (−2, −1). Find the coordinates of A′ and B′ after a dilation with a scale factor of 5 with a center point of dilation at the origin.(1 point)
Responses
A′ (5, 10) and B′ (10, 5)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis 10 comma 5 right parenthesis
A′ (5, 10) and B′ (−2, −1)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 2 comma negative 1 right parenthesis
A′ (5, 10) and B′ (−10, −5)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 10 comma negative 5 right parenthesis
A′ (1, 2) and B′ (−10, −5)
None of the provided responses are correct.
To find the coordinates of A' and B' after dilating with a scale factor of 5 and a center point of dilation at the origin, we can use the formula:
A' = (x, y) * scale factor
Let's calculate the coordinates:
For point A:
x' = 1 * 5 = 5
y' = 2 * 5 = 10
So A'(5, 10).
For point B:
x' = -2 * 5 = -10
y' = -1 * 5 = -5
So B'(-10, -5).
Therefore, the correct answer is:
A' (5, 10) and B' (-10, -5)