Question

1. Given R (7,-1),A(3,-6), B(-3,-6), E(-5,4), plot the points and trace the figure.Part A: Determine the lengths of each side (round to the nearest hundredth).Part B: Determine the perimeter

Answer 1

We are given four points which are as follows

R (7, -1 ), A (3, -6), B(-3, -6) , and E(-5, 4)

Firstly, we will need to represent the points pictorially

Find the point one after the other

Line RE

Where E= (-5, 4) and R = (7, -1)

`\begin{gathered} RE\text{ = }\sqrt[]{(x1-x2)^2+(y1-y2)^2} \\ \text{where x1 = -5, y1 = 4, x2 = 7 and y2 = -1} \\ RE\text{ = }\sqrt[]{(-5-7)^2+(4-(-1)\rbrack^2} \\ RE\text{ = }\sqrt[]{(-12)^2+(4+1)^2} \\ RE\text{ = }\sqrt[]{144\text{ + 25}} \\ RE\text{ = }\sqrt[]{169} \\ RE\text{ = 13 units} \end{gathered}`

For RA

R = (7, -1 ) and A = (3, -6)

`\begin{gathered} RA\text{ = }\sqrt[]{(x1-x2)^2+(y1-y2)^2} \\ \text{Where x1 = 7, y1 = -1, x2 =3 and y2 = -6} \\ RA\text{ = }\sqrt[]{(7-3)^2+(-1-(-6)\rbrack^2} \\ RA\text{ = }\sqrt[]{(4)^2+(-7)^2} \\ RA\text{ = }\sqrt[]{16\text{ + 49}} \\ RA\text{ = }\sqrt[]{65} \\ RA\text{ = 8.06 units} \\ \end{gathered}`

For EB

E = (-5, 4) and B = (-3, -6)

`\begin{gathered} EB\text{ = }\sqrt[]{(x1-x2)^2+(y1-y2)^2} \\ \text{Where x1= -5, y1 = 4, x2 = -3, and y2 = -6} \\ EB\text{ = }\sqrt[]{(-5-(-3)\rbrack^2+(4-(-6^2\text{)\rbrack}} \\ EB\text{ = }\sqrt[]{(-2)^2\text{ + (}}4+6)^2 \\ EB\text{ = }\sqrt[]{4\text{ + 100}} \\ EB\text{ = }\sqrt[]{104} \\ EB\text{ = 10. 20 units} \end{gathered}`

For AB

A (3, -6) and B