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Angle ABC

contains the points A(5,−3)
, B(8,1)
, and C(8,5)
. Describe the effect of the dilation of the angle with a scale factor of 7 and a center point of dilation at the origin (0,0)
. Enter the option number of your response.

Option #1: After dilation, the angle is seven times farther from the point of dilation. The resulting points are A′(35,−21)
, B′(56,7)
, and C′(56,35)
. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle.

Option #2: After dilation, the angle is seven times farther from the point of dilation. The resulting points are A′(12,4)
, B′(15,8)
, and C′(15,12)
. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle.

Option #3: After dilation, the angle is seven times closer to the point of dilation. The resulting points are A′(57,−37)
, B′(87,17)
, and C′(87,57)
. The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle.

(1 point)
Option #

1 answer

To determine the effect of the dilation of angle ABC with the given points A(5,−3), B(8,1), and C(8,5), we need to apply a dilation with a scale factor of 7 centered at the origin (0,0).

Dilation works by multiplying the coordinates of each point by the scale factor.

  1. Calculate the new coordinates after dilation:

    • For point A(5, -3): \[ A' = (5 \times 7, -3 \times 7) = (35, -21) \]
    • For point B(8, 1): \[ B' = (8 \times 7, 1 \times 7) = (56, 7) \]
    • For point C(8, 5): \[ C' = (8 \times 7, 5 \times 7) = (56, 35) \]

  2. Angular properties:

    • The angle measurement remains the same because dilation does not change the angles, just the distance from the center of dilation.
    • The rays of the angle (lines AB and BC) remain parallel to the rays of the dilated angle (lines A'B' and B'C').

Based on this analysis, it aligns with Option #1:

After dilation, the angle is seven times farther from the point of dilation. The resulting points are A′(35,−21), B′(56,7), and C′(56,35). The angle measurement remains the same. Corresponding lines (rays) are parallel between the angle and the dilated angle.

So the correct response is:

Option #1.