Question

the vertices of rhombus defg are d(1, 4), e(4, 0), f(1, -4), and g(-2, 0). what is the perimeter of the rhombus? units

Explanation:

Step1: Calculate the length of one side

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(D(1,4)\) and \(E(4,0)\):
\(x_1 = 1,y_1 = 4,x_2 = 4,y_2 = 0\)
\(DE=\sqrt{(4 - 1)^2+(0 - 4)^2}=\sqrt{3^2+(- 4)^2}=\sqrt{9 + 16}=\sqrt{25}=5\)

Step2: Use the property of a rhombus

Since all sides of a rhombus are equal. Let the side - length be \(a\). Here \(a = 5\)
The perimeter formula of a rhombus is \(P=4a\)
\(P = 4\times5\)

Answer:

\(20\)