Question

which of the following transformations always preserves the dimensions of a figure?
i. translation
ii. rotation
iii. reflection
iv. dilation
a. i, ii, and iii
b. i, ii, and iv
c. i, iii, and iv
d. ii, iii, and iv

Explanation:

Step1: Analyze Translation (I)

Translation moves a figure without changing its size, shape, or dimensions. So it preserves dimensions.

Step2: Analyze Rotation (II)

Rotation turns a figure around a point. It doesn't change the size or shape, so dimensions are preserved.

Step3: Analyze Reflection (III)

Reflection flips a figure over a line. It keeps the size and shape, so dimensions are preserved.

Step4: Analyze Dilation (IV)

Dilation scales a figure by a factor, changing its size (dimensions like length, area may change). So it does not preserve dimensions.

Answer:

A. I, II, and III