Math Snap

STEP 1

1. The distance between two points in a plane can be calculated using the distance formula.
2. The coordinates of Point A are $(0, -2)$.
3. The coordinates of Point C are $(5, 3)$.

STEP 2

1. Identify the coordinates of the points.
2. Apply the distance formula.
3. Calculate the distance.

STEP 3

Identify the coordinates of the points given in the problem. We have:
- Point A: $(0, -2)$
- Point C: $(5, 3)$

STEP 4

Recall the distance formula for two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

STEP 5

Substitute the coordinates of Point A and Point C into the distance formula:
- $x_1 = 0$, $y_1 = -2$
- $x_2 = 5$, $y_2 = 3$
\[
d = \sqrt{(5 - 0)^2 + (3 - (-2))^2} $$

STEP 6

Simplify the expression inside the square root:
\[
d = \sqrt{5^2 + (3 + 2)^2} $$ \[
d = \sqrt{25 + 5^2} $$

STEP 7

Calculate the squares and sum them:
\[
d = \sqrt{25 + 25} $$ \[
d = \sqrt{50} $$

Simplify the square root:
\[
d = \sqrt{50} $$ \[
d = \sqrt{25 \times 2} $$ \[
d = 5\sqrt{2} $$ The distance between Point A and Point C is:
$$\boxed{5\sqrt{2}}$$