Question

multiple choice 5 points
rectangle abcd is shown on the grid.
what is the area of rectangle abcd in square units?
3√17 square units
6√17 square units
17 square units
34 square units

Explanation:

Step1: Find length of AB 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 $A(- 1,4)$ and $B(3,3)$, we have $x_1=-1,y_1 = 4,x_2=3,y_2 = 3$. Then $AB=\sqrt{(3+1)^2+(3 - 4)^2}=\sqrt{16 + 1}=\sqrt{17}$.

Step2: Find length of BC using distance formula

For points $B(3,3)$ and $C(1,-5)$, we have $x_1 = 3,y_1=3,x_2 = 1,y_2=-5$. Then $BC=\sqrt{(1 - 3)^2+(-5 - 3)^2}=\sqrt{(-2)^2+(-8)^2}=\sqrt{4 + 64}=\sqrt{68}=2\sqrt{17}$.

Step3: Calculate area of rectangle

The area of a rectangle $A = l\times w$. Here, if $l = BC$ and $w=AB$, then $A=AB\times BC=\sqrt{17}\times2\sqrt{17}=34$.

Answer:

34 square units