Question

Line AB 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′ (−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 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′ (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 Skip to navigation

Answer 1

To find the coordinates of points A′ and B′ after a dilation with a scale factor of 5 centered at the origin, we can use the following formula for dilation:

\[
A' = (k \cdot x_A, k \cdot y_A)
\]

\[
B' = (k \cdot x_B, k \cdot y_B)
\]

where \( k \) is the scale factor, \( (x_A, y_A) \) are the coordinates of point A, and \( (x_B, y_B) \) are the coordinates of point B.

Given:
- Point A is at (1, 2)
- Point B is at (−2, −1)
- Scale factor \( k = 5 \)

Now we can calculate the coordinates of points A′ and B′.

For point A′:
\[
A' = (5 \cdot 1, 5 \cdot 2) = (5, 10)
\]

For point B′:
\[
B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5)
\]

Thus, the coordinates of A′ and B′ after the dilation are:
- A′ (5, 10)
- B′ (−10, −5)

This corresponds to the second option in the provided responses:
**A′ (5, 10) and B′ (−10, −5)**.