Question

what is the distance between points b and d?
options:
$4\sqrt{6}$ units
$3\sqrt{6}$ units
$5\sqrt{2}$ units
$6\sqrt{2}$ units
points: b(-2,0), c(4,0), d(4,6) (on a grid)

Explanation:

Step1: Identify coordinates of B and D

Point B is at $(-2, 0)$ and point D is at $(4, 6)$.

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 $x_1 = -2$, $y_1 = 0$, $x_2 = 4$, $y_2 = 6$ into the formula:
$$d = \sqrt{(4 - (-2))^2 + (6 - 0)^2}$$

Step3: Simplify the expression

First, calculate the differences: $4 - (-2) = 6$ and $6 - 0 = 6$.
Then, square these differences: $6^2 = 36$ and $6^2 = 36$.
Add the squared differences: $36 + 36 = 72$.
Take the square root: $d = \sqrt{72} = \sqrt{36\times2} = 6\sqrt{2}$.

Answer:

$6\sqrt{2}$ units