Question

find the length and width of the rectangles whose vertices are given. 2.21 a(2,1), b(5,4), c(0,3), d(3,6)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length (e.g., distance between A and B)

Let $A(2,1)$ and $B(5,4)$. Then $d_{AB}=\sqrt{(5 - 2)^2+(4 - 1)^2}=\sqrt{3^2+3^2}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}$.

Step3: Calculate width (e.g., distance between A and C)

Let $A(2,1)$ and $C(0,3)$. Then $d_{AC}=\sqrt{(0 - 2)^2+(3 - 1)^2}=\sqrt{(-2)^2+2^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}$.

Answer:

Length is $3\sqrt{2}$, width is $2\sqrt{2}$