Question

find the area, in square units, of rectangle abcd plotted below. a(-4,5) d(0,6) b(-2,-3) c(2,-2) choose 1 answer: a 14 b 17 c 28 d 34

Explanation:

Step1: Find length of side AD using distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(-4,5)$ and $D(0,6)$, we have $x_1=-4,y_1 = 5,x_2=0,y_2 = 6$. Then $AD=\sqrt{(0 - (-4))^2+(6 - 5)^2}=\sqrt{4^2+1^2}=\sqrt{16 + 1}=\sqrt{17}$.

Step2: Find length of side AB using distance formula

For points $A(-4,5)$ and $B(-2,-3)$, we have $x_1=-4,y_1 = 5,x_2=-2,y_2=-3$. Then $AB=\sqrt{(-2-(-4))^2+(-3 - 5)^2}=\sqrt{2^2+(-8)^2}=\sqrt{4 + 64}=\sqrt{68}=2\sqrt{17}$.

Step3: Calculate area of rectangle

The area of a rectangle $A$ is $A = l\times w$. Here, if we consider $AD$ as width and $AB$ as length, $A=AB\times AD=2\sqrt{17}\times\sqrt{17}=2\times17 = 34$.

Answer:

D. 34