Line AB

contains point A (2, −5)
and point B (−3, −2)
. Find the coordinates of A′
and B′
after a dilation with a scale factor of 4 with a center point of dilation at the origin.(1 point)
Responses

A′ (8, −20)
and B′ (−12, −8)
upper A prime left parenthesis 8 comma negative 20 right parenthesis and upper B prime left parenthesis negative 12 comma negative 8 right parenthesis

A′ (2,−5)
and B′ (−12, −8)
upper A prime left parenthesis 2 comma negative 5 right parenthesis and upper B prime left parenthesis negative 12 comma negative 8 right parenthesis

A′ (8, 20)
and B′ (12, 8)
upper A prime left parenthesis 8 comma 20 right parenthesis and upper B prime left parenthesis 12 comma 8 right parenthesis

A′ (8, −20)
and B′ (−3, −2)

1 answer

To find the coordinates of points A' and B' after a dilation with a scale factor of 4 and center of dilation at the origin (0, 0), we apply the dilation formula:

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

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

  1. For point A (2, -5): \[ A' = (4 \cdot 2, 4 \cdot -5) = (8, -20) \]

  2. For point B (-3, -2): \[ B' = (4 \cdot -3, 4 \cdot -2) = (-12, -8) \]

So, the coordinates after dilation are:

  • A' = (8, -20)
  • B' = (-12, -8)

Thus, the correct response is: A′ (8, −20) and B′ (−12, −8)

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