Question

remedial geometry questions
2 points
△lah is a dilation of △lah about the origin. which statement must be true?
a) the angle measures are preserved, but the side lengths are reduced.
b) the scale factor is k = 2.
c) the scale factor is k = 1/2.
d) the angle measures and side lengths are preserved.

Explanation:

Step1: Recall dilation property

Dilation is a transformation that changes the size but not the shape of a figure. The shape - preservation means angle measures are preserved in a dilation. The side - lengths change by a scale factor \(k\). If \(k> 1\), the figure is enlarged; if \(0 < k<1\), the figure is reduced; if \(k = 1\), the figure is congruent to the original.

Step2: Analyze each option

• Option A: Angle measures are preserved in a dilation. But we don't know if side - lengths are reduced as we don't know the value of \(k\).
• Option B: There is no information given to suggest that \(k = 2\).
• Option C: There is no information given to suggest that \(k=\frac{1}{2}\).
• Option D: In a dilation, angle measures are always preserved. When \(k = 1\), side - lengths are also preserved (in the case of congruent figures which is a special case of dilation). But in general dilation, side - lengths change according to the scale factor \(k

eq1\). However, the most fundamental property of dilation is that angle measures are preserved.

Answer:

A. The angle measures are preserved, but the side lengths are reduced.