Question

Find the perimeter of quadrilateral ABCD with vertices A(0,4), B(4,1), C(1, -3), and D(-3,0).25 units100 units5 units20 units

Answer 1

The perimeter is the sum of the length of each side of the quadrilateral. We would find the length of each side by applying the formula for finding the distance between two points which is expressed as

`\text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

Thus, we have

`\begin{gathered} ForAB,x1=0,y1=4,x2=4,\text{ y2 = 1} \\ \text{Distance = }\sqrt[]{(4-0)^2+(1-4)^2\text{ }}\text{ = }\sqrt[]{16\text{ + 9}} \\ AB\text{ = 5} \\ \text{For BC, x1 = 4, y1 = 1, x2 = 1, y2 = - 3} \\ \text{Distance = }\sqrt[]{(1-4)^2+(-3-1)^2}\text{ = }\sqrt[]{9\text{ + 16}} \\ BC\text{ = 5} \\ \text{For CD, x1 = 1, y1 = - 3, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-1)^2+(0--3)^2}\text{ = }\sqrt[]{16\text{ + 9}} \\ CD\text{ = 5} \\ \text{For AD, x1 = 0, y1 = 4, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-0)^2+(0-4)^2\text{ }}\text{ = }\sqrt[]{9\text{ + 16}} \\ AD\text{ = 5} \end{gathered}`

Perimeter = AB + BC + CD + AD = 5 + 5 + 5 + 5

Perimeter = 20 units