A straight, solid line connects plotted points R and S on a coordinate plane. The line slopes upward from left to right. Point R is left parenthesis negative 4 comma negative 1 right parenthesis. Point S is left parenthesis 1 comma 6 right parenthesis.

Question

How could you calculate the distance between points R
and S
?

(1 point)
Responses

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°
Make line segment cap r cap s 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 line segment cap r cap t .and subtract is from 180 degrees

Subtract x1
from x2
and y1
from y2
. Then divide both values by 2.
Subtract x sub 1 from x sub 2 and y sub 1 from y sub 2 . Then divide both values by 2.

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¯¯¯¯¯¯¯
.
Make line segment cap r cap s 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 line segment cap r cap s .

Subtract x1
from x2
and y1
from y2
. Then multiply both values by 2.
Subtract x sub 1 from x sub 2 and y sub 1 from y sub 2 . Then multiply both values by 2.

Answer 1

To calculate the distance between points \( R(-4, -1) \) and \( S(1, 6) \), the best approach is to treat the line segment \( \overline{RS} \) as the hypotenuse of a right triangle and then apply the Pythagorean Theorem.

Here's a step-by-step breakdown of the process:

1. Calculate the lengths of the legs of the right triangle:

   • The horizontal leg (difference in x-coordinates): \( x_2 - x_1 = 1 - (-4) = 1 + 4 = 5 \)
   • The vertical leg (difference in y-coordinates): \( y_2 - y_1 = 6 - (-1) = 6 + 1 = 7 \)

2. Use the Pythagorean Theorem:

   • According to the Pythagorean Theorem, \( c^2 = a^2 + b^2 \), where \( c \) is the hypotenuse (\( RS \)), and \( a \) and \( b \) are the other two legs of the triangle. Thus, \[ RS = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{5^2 + 7^2} = \sqrt{25 + 49} = \sqrt{74} \]

Considering the responses provided, the correct choice describing this approach is:

Make \( \overline{RS} \) the hypotenuse of a right triangle and calculate the lengths of the triangle's legs on the coordinate plane. Then, use the Pythagorean Theorem to solve for the length of \( \overline{RS} \).