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 the points after dilation, we can use the formula for dilation:

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

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

Given:

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

Now we perform the dilation for each point.

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

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

Thus, the new coordinates are:

• \(A' (5, 10)\)
• \(B' (-10, -5)\)

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