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Question

Solution Steps

1. Understand the question

   a figure is rotated 180 degrees around the origin and then dilated by a scale factor of -2. how will the coordinates of the point $(3, -4)$ change?
   a. $(-6,8)$
   b. $(6,8)$
   c. $(-6,-8)$
   d. $(6,-8)$

2. Explanation

   Step1: Rotate 180° around origin

   For a point $(x,y)$, 180° rotation gives $(-x,-y)$.
   For $(3,-4)$: $(-3, 4)$

   Step2: Dilate by scale factor -2

   Multiply each coordinate by the scale factor: $(-3 \times -2, 4 \times -2)$
   $=(6, -8)$

3. Final answer

   d. (6,−8)

Answer

Question Analysis

OCR Text

a figure is rotated 180 degrees around the origin and then dilated by a scale factor of -2. how will the coordinates of the point $(3, -4)$ change?
a. $(-6,8)$
b. $(6,8)$
c. $(-6,-8)$
d. $(6,-8)$

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