Question

3
drag the tiles to the boxes to form correct pairs.
polygon abcd has sides with these lengths: $overline{ab}$ 5 units; $overline{bc}$, 4 units; $overline{cd}$, 4.5 units; and $overline{ad}$, 7 units. the slope of $overline{ab}$ is 5, the slope of $overline{bc}$ is 0.25, the slope of $overline{cd}$ is -2, and the slope of $overline{ad}$ is 0. the polygon is dilated from point a by a scale factor of 1.2 to form polygon abcd. match the slopes and lengths of the sides of polygon abcd to their values.
slope of $overline{ab}$
6.4
length of $overline{cd}$
5.4
length of $overline{ad}$
5
slope of $overline{bc}$
0.25

Explanation:

Step1: Recall dilation properties

Dilation preserves slopes of sides, scales lengths by the scale factor $k=1.2$.

Step2: Match slopes (no change)

Slope of $\overline{A'B'}$ = Slope of $\overline{AB} = 5$
Slope of $\overline{B'C'}$ = Slope of $\overline{BC} = 0.25$

Step3: Calculate length of $\overline{A'D'}$

$\text{Length of } \overline{A'D'} = 7 \times 1.2 = 8.4$

Step4: Calculate length of $\overline{C'D'}$

$\text{Length of } \overline{C'D'} = 4.5 \times 1.2 = 5.4$

Answer:

1. slope of $\overline{A'B'}$ $\longleftrightarrow$ 5
2. length of $\overline{A'D'}$ $\longleftrightarrow$ 8.4
3. length of $\overline{C'D'}$ $\longleftrightarrow$ 5.4
4. slope of $\overline{B'C'}$ $\longleftrightarrow$ 0.25