A drone begins at point P and flies directly north for 24 meters to point Q. It then turns… — ACT

A drone begins at point $P$ and flies directly north for $24$ meters to point $Q$ . It then turns directly east and flies for $10$ meters to point $R$ . From point $R$ , the drone flies along a straight path directed $45^\circ$ south of east until it reaches point $S$ , which lies directly east of starting point $P$ . What is the distance, in meters, from point $P$ to point $S$ ?

Answer: 34 meters

Answer

The total distance from point P to point S is 34 meters.

Flying north 24 meters places point R at a height of 24 meters above the horizontal line passing east through P. Returning to this horizontal line at point S along a path 45° south of east forms a 45°-45°-90° right triangle with a vertical leg of 24 meters. Because the legs of a 45°-45°-90° right triangle are congruent, the horizontal leg is also 24 meters. Combining this with the initial 10 meters of eastward travel gives a total distance from P to S of 10 + 24 = 34 meters.

Step-by-Step Solution

Determine the vertical and horizontal position of point R relative to point P.

Point R is located 24 meters north and 10 meters east of point P.

The flight 24 meters north sets the vertical distance to 24 meters, and the flight 10 meters east sets the horizontal displacement to 10 meters.

Apply the properties of a 45°-45°-90° special right triangle to find the horizontal distance from point R to point S.

The horizontal distance traveled between point R and point S is 24 meters.

Since point S lies directly east of point P (at vertical height 0), the vertical drop from point R to point S is 24 meters. A line angled 45° south of east creates a 45°-45°-90° right triangle whose two leg lengths are equal, so the horizontal leg length equals the vertical leg length of 24 meters.

Calculate the total horizontal distance from point P to point S.

34 meters

Sum the initial east displacement of 10 meters from P to R with the additional horizontal displacement of 24 meters from R to S: 10 + 24 = 34 meters.

Key Concept

45°-45°-90° Special Right Triangle Properties and Planar Displacement

Estimated Time:1m 30s

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