Question

Polygon abcd has sides with these lengths: ab, 5 units; bc, 4 units; cd, 4.5 units; and ad, 7 units. The polygon is dilated from point a by a scale factor of 1.2 to form polygon a′b′c′d′. Match the slopes and lengths of the sides of polygon a′b′c′d′ to their values.

Option 1: Slope of a' b' = 5; Length of c' d' = 5.4; Length of a' d' = 5; Slope of b' c' = 0.25
Option 2: Slope of a' b' = 0.25; Length of c' d' = 5.4; Length of a' d' = 5; Slope of b' c' = 5
Option 3: Slope of a' b' = 5; Length of c' d' = 4.5; Length of a' d' = 7; Slope of b' c' = 0.25
Option 4: Slope of a' b' = 0.25; Length of c' d' = 4; Length of a' d' = 5; Slope of b' c' = 5

Answer 1

None of the provided options match the result of dilating the given polygon's sides by a scale factor of 1.2. The slopes of sides do not change with dilation, and without further details, the slopes listed in the options cannot be validated.Therefore, the correct option is Option 4:

Step-by-step explanation:

The question involves a dilation of a polygon from a point with a given scale factor, and we need to determine the slopes and lengths of the sides of the new polygon. We would do this by applying the scale factor to each side length of the original polygon to find the side lengths of the dilated polygon. However, we must remember that dilation affects lengths but does not affect the slopes of the sides because they are determined by the angle between the sides, which remains constant during dilation.

Therefore, the slopes of the corresponding sides should be the same before and after the dilation. The correct match for the sides of the dilated polygon for the polygon with sides AB=5, BC=4, CD=4.5, AD=7, and a dilation factor of 1.2 would be: Length of A'B' = 5 * 1.2 = 6 units; Length of B'C' = 4 * 1.2 = 4.8 units; Length of C'D' = 4.5 * 1.2 = 5.4 units; and Length of A'D' = 7 * 1.2 = 8.4 units.

However, none of these lengths are listed in the given options correctly. Also, the options provided about slopes do not seem to relate to specific side lengths or pairs of points to calculate their slopes. Therefore, without additional information about the coordinates of the points or the orientation of the sides, the slopes cannot be accurately matched with the given options.Therefore, the correct option is Option 4: