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Math  /  Geometry

Question3 . Find the distance between point AA and Point CC on the graph below.
Distance == □\square units

Studdy Solution

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) (0, -2) .
3. The coordinates of Point C are (5,3) (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) (0, -2) - Point C: (5,3) (5, 3)

STEP 4

Recall the distance formula for two points (x1,y1) (x_1, y_1) and (x2,y2) (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: - x1=0 x_1 = 0 , y1=−2 y_1 = -2 - x2=5 x_2 = 5 , y2=3 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} $

STEP 8

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:
52 \boxed{5\sqrt{2}}

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