Line AB

Question

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′ (1, 2)
and B′ (−10, −5)
upper A prime left parenthesis 1 comma 2 right parenthesis and upper B prime left parenthesis negative 10 comma negative 5 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 10 comma 5 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′ (5, 10)
and B′ (−2, −1)

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after a dilation with a scale factor of 5 about the origin, we can use the dilation formula:

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

where \( (x', y') \) are the coordinates after dilation, \( (x, y) \) are the original coordinates, and \( k \) is the scale factor.

1. For point \( A(1, 2) \):

   • Dilation: \[ A' = (5 \cdot 1, 5 \cdot 2) = (5, 10) \]

2. For point \( B(-2, -1) \):

   • Dilation: \[ B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5) \]

Thus, after dilation, we have:

• \( A' (5, 10) \)
• \( B' (-10, -5) \)

Therefore, the correct response is:

A′ (5, 10) and B′ (−10, −5)