Question

Which of the following statements about dilations is true?

a) Dilations always increase the length of line segments.
b) Dilations take perpendicular lines to perpendicular lines.
c) Dilations of an angle are congruent to the original angle.
d) Dilations increase the measure of angles.

Answer 1

Dilations can either increase or decrease the length of line segments, take perpendicular lines to perpendicular lines, dilations of an angle do not result in congruent angles, and dilations do not increase the measure of angles.

Step-by-step explanation:

In dilations, line segments can either increase or decrease in length depending on the scale factor. So, statement a) is not always true.

Dilations do take perpendicular lines to perpendicular lines. This is because the angle between two lines is preserved in a dilation. So, statement b) is true.

Dilations of an angle do not always result in congruent angles. The measure of an angle can increase or decrease depending on the scale factor. So, statement c) is false.

In dilations, angles are not increased. They are preserved. So, statement d) is false.