Question

The points q (-1,-8), r (-8,-9), and s (-9,-2) form a triangle. Find the desired slope and lengths.

Answer 1

The slope of the sides of the triangle are 1/7, -7, and -3/4. The lengths of the sides of the triangle are 5sqrt(2), 5sqrt(2), and 10.

Step-by-step explanation:

First, we can find the slopes of the sides of the triangle using the formula:

slope = (y2 - y1) / (x2 - x1)

For the side QR: slope = (-9 - (-8)) / (-8 - (-1)) = -1 / -7 = 1/7

For the side RS: slope = (-2 - (-9)) / (-9 - (-8)) = 7 / -1 = -7

For the side SQ: slope = (-2 - (-8)) / (-9 - (-1)) = 6 / -8 = -3/4

Next, we can find the lengths of the sides of the triangle using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For the side QR: distance = sqrt((-8 - (-1))^2 + (-9 - (-8))^2) = sqrt(49 + 1) = sqrt(50) = 5sqrt(2)

For the side RS: distance = sqrt((-9 - (-8))^2 + (-2 - (-9))^2) = sqrt(1 + 49) = sqrt(50) = 5sqrt(2)

For the side SQ: distance = sqrt((-9 - (-1))^2 + (-2 - (-8))^2) = sqrt(64 + 36) = sqrt(100) = 10