Question

Nasir is laying out a garden in the shape of a right triangle. He draws it on the coordinate grid below. The three vertices of his garden are at the points A(-3,-4), B(6,-4), and C(6,8). He wants to enclose the garden with a fence that runs along its perimeter. How many feet of fencing will Nasir need? A) 36 ft of fencing B) 9 ft of fencing C) 12 ft of fencing D) 225 ft of fencing

Answer 1

To solve this problem, we find the distance between the lines using the coordinate points

Considering the diagram above, we will find the distance of Line AC, Line AB, and Line BC respectively

The expression from the length of a line given coordinate points is

`\text{Length of line = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Where for Line AB

`\begin{gathered} x_2=6 \\ x_1=-3 \\ y_2=-4 \\ y_1_{}=\text{ -4} \\ Line\text{ AB = }\sqrt[]{(6-(-3))^2+(-4-(-4))^2} \end{gathered}`
`\begin{gathered} \text{Line AB = }\sqrt[]{(6+3)^2} \\ \text{Line AB = }\sqrt[]{9^2} \\ Line\text{ AB = 9} \end{gathered}`

Line AC

x1=-3

x2=6

y1=-4

y2=8

`\begin{gathered} AC\text{ = }\sqrt[]{(6-(-3))^2+((8-(-4))^2} \\ AC\text{ =}\sqrt[]{9^2+12^2} \\ AC\text{ =}\sqrt[]{81\text{ + 144}} \\ AC\text{ =}\sqrt[]{225} \\ AC\text{ =15} \end{gathered}`

Line BC

x1=6

x2=6

y2=8

y1=-4

`\begin{gathered} BC\text{ = }\sqrt[]{(6-6)^2+(8-(-4))^2} \\ BC\text{ =}\sqrt[]{12^2} \\ BC\text{ = 12} \end{gathered}`

The perimeter of the fence will therefore be, the sum of all the sides

= BC + AC + AB

= 12 + 15 + 9= 36 ft of fencing

Hence option A is the answer