Question

multiple choice 1 point a rectangle has the following vertices: a(-1, 9), b(0, 9), c(0, -8), d(-1, -8). what is the perimeter of rectangle abcd? 34 units 18 units 17 units 36 units

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: Find length of one - side

Let's find the distance between $A(-1,9)$ and $B(0,9)$. Using the distance formula, with $x_1=-1,y_1 = 9,x_2 = 0,y_2 = 9$, we have $d_{AB}=\sqrt{(0 - (-1))^2+(9 - 9)^2}=\sqrt{1+0}=1$.

Step3: Find length of adjacent - side

Let's find the distance between $B(0,9)$ and $C(0,-8)$. Using the distance formula, with $x_1 = 0,y_1 = 9,x_2 = 0,y_2=-8$, we have $d_{BC}=\sqrt{(0 - 0)^2+(-8 - 9)^2}=\sqrt{0 + (-17)^2}=17$.

Step4: Calculate perimeter of rectangle

The perimeter of a rectangle $P = 2(l + w)$, where $l$ and $w$ are the length and width of the rectangle. Here $l = 17$ and $w = 1$, so $P=2(17 + 1)=36$.

Answer:

36 units