Question

a quadrilateral abcd has vertices a(0,0), b(5,0), c(5,2) and d(0,2).
determine the slope and distance for each side of abcd.
*write your distances as decimals.
slope of ab =
slope of bc =
slope of cd =
slope of ad =
ab =
bc =

Explanation:

Step1: Slope formula for AB

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
For $A(0,0), B(5,0)$: $m_{AB}=\frac{0-0}{5-0}=0$

Step2: Slope formula for BC

For $B(5,0), C(5,2)$: $m_{BC}=\frac{2-0}{5-5}=\frac{2}{0}$ (undefined)

Step3: Slope formula for CD

For $C(5,2), D(0,2)$: $m_{CD}=\frac{2-2}{0-5}=0$

Step4: Slope formula for AD

For $A(0,0), D(0,2)$: $m_{AD}=\frac{2-0}{0-0}=\frac{2}{0}$ (undefined)

Step5: Distance formula for AB

Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
For $A(0,0), B(5,0)$: $d_{AB}=\sqrt{(5-0)^2+(0-0)^2}=5.0$

Step6: Distance formula for BC

For $B(5,0), C(5,2)$: $d_{BC}=\sqrt{(5-5)^2+(2-0)^2}=2.0$

Answer:

Slope of AB = 0
Slope of BC = undefined
Slope of CD = 0
Slope of AD = undefined
AB = 5.0
BC = 2.0