Answer:
[tex]m = 3[/tex] ---- Slopes of QU and AD
[tex]m =\frac{2}{3}[/tex] ---- Slopes of UA and QD
Sides QU and AD have the same slope
Sides UA and QD have the same slope
Step-by-step explanation:
Given
[tex]Q = (1, 2)[/tex]
[tex]U = (2, 5)[/tex]
[tex]A = (5, 7)[/tex]
[tex]D = (4, 4)[/tex]
Solving (a): Slope of QU
[tex]Q = (x_1,y_1)= (1, 2)[/tex]
[tex]U = (x_2,y_2)= (2, 5)[/tex]
Slope, m is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m =\frac{5-2}{2-1}[/tex]
[tex]m =\frac{3}{1}[/tex]
[tex]m = 3[/tex]
Slope of AD
[tex]A =(x_1,y_1) = (5, 7)[/tex]
[tex]D = (x_2,y_2) = (4, 4)[/tex]
Slope, m is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m =\frac{4-7}{4-5}[/tex]
[tex]m =\frac{-3}{-1}[/tex]
[tex]m = 3[/tex]
Slope of UA
[tex]A =(x_1,y_1) = (5, 7)[/tex]
[tex]U = (x_2,y_2)= (2, 5)[/tex]
Slope, m is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m =\frac{5-7}{2-5}[/tex]
[tex]m =\frac{-2}{-3}[/tex]
[tex]m =\frac{2}{3}[/tex]
Slope of QD
[tex]Q = (x_1,y_1)= (1, 2)[/tex]
[tex]D = (x_2,y_2) = (4, 4)[/tex]
Slope, m is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m =\frac{4-2}{4-1}[/tex]
[tex]m =\frac{2}{3}[/tex]
Solving (b): Parallel Sides
Two sides are said to be parallel if they have the same slope.
The slope were calculated in (a) above and from there, we have the following observations
1. QU and AD have the same slope of 3
2. UA and QD have the same slope of 2/3
