Question

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) 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′ (−5, −2) and B′ (−2, 6) upper A prime left parenthesis negative 5 comma negative 2 right parenthesis and upper B prime left parenthesis negative 2 comma 6 right parenthesis A′ (−8, 2) and B′ (−2, 6)

Answer 1

To find the coordinates of A′ and B′ after a dilation with a scale factor of 2 from the origin, we use the following formula for dilation:

If a point \(P(x, y)\) is dilated from the origin with a scale factor \(k\), the new coordinates \(P′(x′, y′)\) are given by: \[ x′ = k \cdot x \] \[ y′ = k \cdot y \]

For point A(−4, 1):

• Using the scale factor \(k = 2\): \[ x′ = 2 \cdot (-4) = -8 \] \[ y′ = 2 \cdot 1 = 2 \] So, \(A′(-8, 2)\).

For point B(−1, 3):

• Using the same scale factor \(k = 2\): \[ x′ = 2 \cdot (-1) = -2 \] \[ y′ = 2 \cdot 3 = 6 \] So, \(B′(-2, 6)\).

Therefore, after the dilation, the coordinates are:

• \(A′(-8, 2)\)
• \(B′(-2, 6)\)

Looking at the available responses, the correct answer is: A′ (-8, 2) and B′ (-2, 6).