Question

d(-2,5) c(-5,1) a(1,1) b(-2,-3) what is the perimeter of rhombus abcd? 10 units 20 units 2√7 units 4√7 units

Explanation:

Step1: Find the length of side AC or AD (using distance formula)

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let's find the length of side \(AD\). Points \(A(1,1)\) and \(D(-2,5)\).
So, \(x_1 = 1,y_1 = 1,x_2=-2,y_2 = 5\).
\(AD=\sqrt{(-2 - 1)^2+(5 - 1)^2}=\sqrt{(-3)^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5\)

Step2: Calculate the perimeter of the rhombus

In a rhombus, all sides are equal. So perimeter \(P = 4\times\) side length.
Since side length is 5, perimeter \(P=4\times5 = 20\)

Answer:

20 units