Question

(Pythagorean Theorem and the Coordinate Plane MC)

Runners at a cross-country meet run 3 miles north and then 5 miles west from the starting line. Determine the shortest straight path they must run to get back to the starting line.
√8 miles
O 4 miles
miles
O 8 miles

Answer 1

The shortest straight path back to the starting line is 5 miles.

Step-by-step explanation:

To determine the shortest straight path back to the starting line, we can represent the runners' movements on a coordinate plane. Start by assigning the starting point as the origin (0,0). The first leg of the journey is 3 miles north, so the coordinates for that point are (0,3). The second leg is 5 miles west, so the coordinates for that point are (-5,3). To determine the shortest path back to the origin, we can use the distance formula, which is based on the Pythagorean Theorem. The distance formula is:

d = √((x2-x1)2 + (y2-y1)2)

Using the coordinates (0,3) and (-5,3), we can substitute those values into the formula:

d = √((0-(-5))2 + (3-3)2) = √(52 + 0) = √25 = 5 miles

Therefore, the shortest straight path the runners must run to get back to the starting line is 5 miles.

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