Question

Determine the length of each side of quadrilateral ABCD.Side ABSide CDSide AD

Answer 1

To answer this question we will use the following formula for the distance between two points:

`d=_{}\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}.`

From the given graph we get that:

`\begin{gathered} A=(2,-3), \\ B=(2,2), \\ C=(4,1), \\ D=(4,-3)\text{.} \end{gathered}`

Therefore:

1)

`\begin{gathered} \bar{AB}=\sqrt[]{(2-2)^2+(-3-2)^2} \\ =\sqrt[]{(-5)^2}=|-5|=5. \end{gathered}`

2)

`\begin{gathered} \bar{CD}=\sqrt[]{(4-4)^2+(-3-1)} \\ \sqrt[]{(-4)^2}=|-4|=4. \end{gathered}`

3)

`\begin{gathered} \bar{AD}=\sqrt[]{(4-2)^2+(-3-(-3))} \\ =\sqrt[]{2^2}=|2|=2. \end{gathered}`

4)

`\begin{gathered} \bar{BC}=\sqrt[]{(4-2)^2+(1-2)^2} \\ =\sqrt[]{2^2+(-1)^2}=\sqrt[]{4+1}=\sqrt[]{5}\text{.} \end{gathered}`

Answer:

`\begin{gathered} \bar{AB}=5, \\ \bar{BC}=\sqrt[]{5}, \\ \bar{CD}=4, \\ \bar{AD}=2. \end{gathered}`