On a coordinate map, two tracking stations are located at the points (2, -3) and (-6, 12).… — ACT

On a coordinate map, two tracking stations are located at the points $(2, -3)$ and $(-6, 12)$ . What is the straight-line distance, in map units, between the two stations?

Answer: 17 map units

Answer

The straight-line distance between the two stations is 17 map units.

Applying the coordinate distance formula to the coordinates

(2, -3)

and

(-6, 12)

yields a distance of

\sqrt{(-6 - 2)^2 + (12 - (-3))^2} = \sqrt{(-8)^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17

Step-by-Step Solution

Identify coordinates of the two stations.

(x_1, y_1) = (2, -3)

and

(x_2, y_2) = (-6, 12)

Defining the coordinate variables is necessary to apply the formula correctly.

Apply the distance formula.

d = \sqrt{(-6 - 2)^2 + (12 - (-3))^2}

The distance formula calculates the straight-line distance between two coordinates.

Simplify the arithmetic terms.

d = \sqrt{(-8)^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289}

Simplify the differences and squares under the radical.

Calculate the final square root.

d = 17

The square root of 289 is 17.

Key Concept

Distance Formula

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