Question

How could you calculate the distance between points R and S?
Point R: (-4, -1)
Point S: (1, 6)

A. Make RS the leg of a non-right triangle on the coordinate plane by adding point T. Then, use the Pythagorean Theorem to solve for the length of RT and subtract is from 180 degrees
B. Subtract x_1 from x_2 and y_1 from y_2. Then multiply both values by 2.
C. Make RS the hypotenuse of a right triangle and calculate the lengths of the triangles' legs on the coordinate plane. Then, use the Pythagorean Theorem to solve for the length of RS.

Answer 1

To calculate the distance between points R (-4, -1) and S (1, 6), you should use option C. Here’s how you would do it:

1. Identify the coordinates of the points:
- Point R: \( R(-4, -1) \)
- Point S: \( S(1, 6) \)

2. Calculate the lengths of the legs of a right triangle formed by the points R and S:
- The difference in the x-coordinates: \( x_2 - x_1 = 1 - (-4) = 1 + 4 = 5 \)
- The difference in the y-coordinates: \( y_2 - y_1 = 6 - (-1) = 6 + 1 = 7 \)

3. Use the Pythagorean theorem where \( a^2 + b^2 = c^2 \), with \( a \) and \( b \) as the lengths of the legs, and \( c \) as the hypotenuse (the distance RS).
- Here, \( a = 5 \) and \( b = 7 \).
- Calculate \( c \):
\[
c = \sqrt{5^2 + 7^2} = \sqrt{25 + 49} = \sqrt{74}
\]

4. The distance between points R and S is \( \sqrt{74} \).

Therefore, the correct option for calculating the distance RS is **C**.