Line AB contains point A(−4, 1) and point B (−1, 3). Find the coordinates of A′ and B′ after a dilation with a scale factor of 2 with a center point of dilation at the origin.(1 point)

Question

Responses

A′ (8, −2) and B′ (2, −6)
upper A prime left parenthesis 8 comma negative 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis

A′ (−8, 2) and B′ (2, −6)
upper A prime left parenthesis negative 8 comma 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis

A′ (−8, 2) and B′ (−2, 6)
upper a prime left parenthesis negative 8 comma 2 right parenthesis and upper b prime left parenthesis negative 2 comma 6 right parenthesis

A′ (−5, −2) and B′ (−2, 6)

Answer 1

To perform a dilation of points A and B with a scale factor of 2 from the origin, we apply the following formula for dilation:

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

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

In this case, the scale factor \( k = 2 \).

For point A(-4, 1): \[ x' = 2 \cdot (-4) = -8 \] \[ y' = 2 \cdot 1 = 2 \]

So, the coordinates of A' are A'(-8, 2).

For point B(-1, 3): \[ x' = 2 \cdot (-1) = -2 \] \[ y' = 2 \cdot 3 = 6 \]

So, the coordinates of B' are B'(-2, 6).

The final coordinates after dilation are:

• A'(-8, 2)
• B'(-2, 6)

The correct response is: A′ (−8, 2) and B′ (−2, 6).