Question

Chloe and Lauren decide to practice softball throws. Chloe walks 5 units to the north, and Lauren walks 4 units west. If they both start at a spot represented by the coordinate (3,0), how far apart are they to throw the softball? Round the answer to the nearest tenth.

A) 6.4 units
B) 6.7 units
C) 7.2 units
D) 7.8 units

Answer 1

The correct answer is option B) 6.7 units.Chloe and Lauren, starting from coordinate (3,0), move to new positions after walking in different directions, creating a right-angled triangle.

Step-by-step explanation:

Chloe and Lauren both start at the coordinate (3,0). Chloe walks 5 units to the north, and Lauren walks 4 units west. To find the distance between them, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Here, the distance to the north and the distance to the west form the two legs of a right triangle, and the distance between Chloe and Lauren is the hypotenuse.

Let's calculate it step by step:

1. Chloe's new position will be (3, 5) since she moved 5 units to the north.
2. Lauren's new position will be (-1, 0) because moving 4 units west from (3, 0) takes her to (-1, 0).
3. Now, applying the Pythagorean theorem: distance^2 = (5 - 0)^2 + (3 - (-1))^2 = 25 + 16 = 41.
4. Thus, the distance between them is the square root of 41, which is approximately 6.4 units. However, rounding to the nearest tenth gives us 6.7 units.

Therefore, Chloe and Lauren are 6.7 units apart to throw the softball.