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

A. 8 units

Explanation:

Coordinates of A = (-2, -2)

Coordinates of C = (5, 2)

Use distance formula,
`d = √((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 = √((5 -(-2))^2 + (2 -(-2))^2)`

`d = √((7)^2 + (4)^2)`

`d = √(49 + 16) = √(65)`

`d = 8.1` (nearest tenth)

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