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′ (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′ (−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′ (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 centered at the origin, you can use the formula for dilation:

\[ (x', y') = (kx, ky) \]

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

Given:

• Point A(1, 2)
• Point B(−2, −1)
• Scale factor \(k = 5\)

Now, we can calculate the new coordinates.

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

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

Therefore, the coordinates after the dilation are:

• \(A' (5, 10)\)
• \(B' (-10, -5)\)

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