Question

what is the perimeter of rhombus abcd? 4√7 units 10 units 20 units 2√7 units

Explanation:

Step1: Recall side - length property of rhombus

All sides of a rhombus are equal. So, find the length of one side using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Select two points

Let's find the distance between points $A(1,1)$ and $B(-2,-3)$. Here $x_1 = 1,y_1 = 1,x_2=-2,y_2 = - 3$.

Step3: Apply the distance formula

$d=\sqrt{(-2 - 1)^2+(-3 - 1)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step4: Calculate the perimeter

Since the perimeter $P$ of a rhombus with side - length $s$ is $P = 4s$, and $s = 5$, then $P=4\times5 = 20$.

Answer:

20 units