Question

1. trapezoid abcd is shown. which measurement is closest to the length of diagonal bd in units?

8.5 units
10 units
14 units
18.5 units
clear all

Explanation:

Step1: Identify coordinates of B and D

From the grid: $B=(5,2)$, $D=(-3,8)$

Step2: Apply distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Substitute the coordinates:
$BD=\sqrt{(5-(-3))^2+(2-8)^2}$

Step3: Calculate differences

Compute the terms inside the square root:
$\sqrt{(8)^2+(-6)^2}=\sqrt{64+36}$

Step4: Simplify the expression

Add and take the square root:
$\sqrt{100}=10$

Answer:

10 units