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′ (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)
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 10 comma 5 right parenthesis

A′ (1, 2)
and B′ (−10, −5)

Answer 1

To find the coordinates of points A' and B' after a dilation with a scale factor of 5 from the origin, we will use the formula for dilation:

\[ A' = (kx, ky) \] \[ B' = (kx, ky) \]

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

For point A(1, 2):

• Scale factor \( k = 5 \)
• The new coordinates will be: \[ A' = (5 \cdot 1, 5 \cdot 2) = (5, 10) \]

For point B(-2, -1):

• Scale factor \( k = 5 \)
• The new coordinates will be: \[ B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5) \]

Thus, the coordinates after dilation are:

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

Therefore, the correct response is: A′ (5, 10) and B′ (−10, −5).