Question

Polygon ABCD has sides with these lengths: AB, 5 units; BC, 4 units; CD, 4.5 units; and AD, 7 units. The slope of AB is 5, the slope of BC is 0.25, the slope of CD is -2, and the slope of AD is 0. The polygon is dilated from point A by a scale factor of 1.2 to form polygon A'BCD. Match the slopes and lengths of the sides of polygon A'BCD to their values.

A. AB' = 6 units, BC' = 4.8 units, CD' = 5.4 units, AD' = 8.4 units
B. AB' = 5.5 units, BC' = 5 units, CD' = 6 units, AD' = 9 units
C. AB' = 5 units, BC' = 4 units, CD' = 4.5 units, AD' = 7 units
D. AB' = 6 units, BC' = 5 units, CD' = 4 units, AD' = 7 units

Answer 1

After a dilation with a scale factor of 1.2, the lengths of the sides of the polygon A'BCD are multiplied by 1.2 while the slopes remain unchanged. The new side lengths are AB'=6 units, BC'=4.8 units, CD'=5.4 units, AD'=8.4 units, which corresponds to option A.

Step-by-step explanation:

The question deals with the concept of dilations in geometry, where a polygon is enlarged by a specific scale factor. The slopes of the sides are provided for polygon ABCD, and after dilation by a scale factor of 1.2 from point A, we want to match the new lengths and slopes of the sides of the resulting polygon A'BCD.

In a dilation, the slopes of the sides of a polygon remain unchanged, because the dilation stretches the polygon uniformly in all directions, thus not altering the angles between the sides. The lengths of the sides, however, will be multiplied by the scale factor. Therefore, we calculate the new lengths: AB' = AB × 1.2 = 5 × 1.2 = 6 units, BC' = BC × 1.2 = 4 × 1.2 = 4.8 units, CD' = CD × 1.2 = 4.5 × 1.2 = 5.4 units, and AD' = AD × 1.2 = 7 × 1.2 = 8.4 units. Therefore, the correct match for the slopes and lengths of the sides of polygon A'BCD is option A.