Question

3. Rectangle ABCD is shown on the coordinate grid below.
у
10
8 units
12 units
- 10 -8
X
9 units
D
o
7 units

Which is closest to the length of diagonal
AC?

Answer 1

Answer:

A. 8 units

Step-by-step explanation:

Coordinates of A = (-2, -2)

Coordinates of C = (5, 2)

Use distance formula, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ to calculate the length of diagonal $\overline{AC}$.

Let,

$A(-2, -2) = (x_1, y_1)$

$C(5, 2) = (x_2, y_2)$

$d = \sqrt{(5 -(-2))^2 + (2 -(-2))^2}$

$d = \sqrt{(7)^2 + (4)^2}$

$d = \sqrt{49 + 16} = \sqrt{65}$

$d = 8.1$ (nearest tenth)

Therefore, the closest to the length of diagonal $\overline{AC} = 8 units$