Line AB

Question

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 negative 2 comma 6 right parenthesis

A′ (−5, −2)
and B′ (−2, 6)
upper A prime left parenthesis negative 5 comma negative 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 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)

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after a dilation with a scale factor of 2 centered at the origin, we apply the dilation formula:

\[ (x', y') = (kx, ky) \]

where \( k \) is the scale factor, and \((x, y)\) are the original coordinates of the points.

For point A(-4, 1):

• Dilation with scale factor \( k = 2 \): \[ A' = (2 \cdot -4, 2 \cdot 1) = (-8, 2) \]

For point B(-1, 3):

• Dilation with scale factor \( k = 2 \): \[ B' = (2 \cdot -1, 2 \cdot 3) = (-2, 6) \]

Therefore, the coordinates after dilation are:

• \( A'(-8, 2) \)
• \( B'(-2, 6) \)

The correct response is: A′ (−8, 2) and B′ (−2, 6).