Select the coordinates A′

Question

and B′
after dilation of the line segment AB
with a scale factor of 4, centered at the origin where the endpoints are A(−2,−3)
and B (−4,−5)
.(1 point)
Responses

A′ (8,12)
and B′(16,20)
upper A prime left parenthesis 8 comma 12 right parenthesis and upper B prime left parenthesis 16 comma 20 right parenthesis

A′(−8,−12)
and B′(−16,−20)
upper A prime left parenthesis negative 8 comma negative 12 right parenthesis and upper B prime left parenthesis negative 16 comma negative 20 right parenthesis

A′ (−8,−12)
and B′ (−4,−5)
upper A prime left parenthesis negative 8 comma negative 12 right parenthesis and upper B prime left parenthesis negative 4 comma negative 5 right parenthesis

A′ (−2, 3)
and B′ (−4,−5)

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after dilation with a scale factor of 4 centered at the origin, we use the formula for dilation:

\[ (x', y') = (k \cdot x, k \cdot y) \]

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

1. For point \( A(-2, -3) \): \[ A' = (4 \cdot -2, 4 \cdot -3) = (-8, -12) \]

2. For point \( B(-4, -5) \): \[ B' = (4 \cdot -4, 4 \cdot -5) = (-16, -20) \]

Thus, the coordinates after dilation are:

• \( A'(-8, -12) \)
• \( B'(-16, -20) \)

The correct response is:

A′(−8,−12) and B′(−16,−20).