Question

figure mnop is plotted on a coordinate plane. it is rotated 180 degrees clockwise about the origin and then dilated by a scale factor of 0.5 to get image mnop.
which statement must be true of the two figures?
a the figures are congruent because of a reduction in the original figure.
b the figures are similar because of an enlargement in the original figure.
c the figures are congruent because of enlargement in the original figure.
d the figures are similar because of a reduction in the original figure.

Explanation:

Step1: Understand congruent and similar figures

Congruent figures have the same shape and size. Similar figures have the same shape but different sizes. A rotation is a transformation that turns a figure around a point. A dilation is a transformation that changes the size of a figure. A scale factor of \(0.5\) means the image is a reduction (since \(0.5<1\)).

Step2: Analyze each option

• Option A and C: Congruent figures must have the same size. Since there is a dilation (scale factor \(0.5\)), the figures are not congruent. So A and C are wrong.
• Option B: An enlargement has a scale factor \(k > 1\). Here the scale factor is \(0.5<1\) (a reduction), so B is wrong.
• Option D: Since the transformation is a rotation (which preserves shape) and a dilation (scale factor \(0.5\) - a reduction in size), the figures are similar.

Answer:

D. The figures are similar because of a reduction in the original figure.