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 $A^{\prime }$ and $B^{\prime }$ after dilation with a scale factor of 4 centered at the origin, we use the formula for dilation:

$$(x^{\prime },y^{\prime })=(k\cdot x,k\cdot y)$$

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

1. For point $A(-2,-3)$: $$A^{\prime }=(4\cdot -2,4\cdot -3)=(-8,-12)$$

2. For point $B(-4,-5)$: $$B^{\prime }=(4\cdot -4,4\cdot -5)=(-16,-20)$$

Thus, the coordinates after dilation are:

• $A^{\prime }(-8,-12)$
• $B^{\prime }(-16,-20)$

The correct response is:

A′(−8,−12) and B′(−16,−20).