The slopes of the indicated sides of the quadrilateral using the formula for the slope of a line between two points (x1, y1) and (x2, y2), which is (y2 - y1) / (x2 - x1) are:
Side 1: 1/3
Side 2: -2
Side 3: 1/3
Side 4: -2.
The slope measures the steepness of a line, usually denoted by the letter m.
The slope represents the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line.
Slope Formula:
(x1, y1) and (x2, y2), which is (y2 - y1) / (x2 - x1).
The indicated sides of the quadrilateral are:
Side 1: (0,−5) to (6,−3)
Side 2: (6,−3) to (4,1)
Side 3: (4,1) to (−2,−1)
Side 4: (−2,−1) to (0,−5)
Using the slope formula for each side:
Slope of Side 1 = (−3 - (−5)) / (6 - 0) = 2 / 6 = 1/3
Slope of Side 2 = (1 - (−3)) / (4 - 6) = 4 / (−2) = -2
Slope of Side 3 = (−1 - 1) / (−2 - 4) = −2 / (−6) = 1/3
Slope of Side 4 = (−5 - (−1)) / (0 - (−2)) = −4 / 2 = −2
Thus, the slopes of the indicated sides of the quadrilateral are:
Side 1: 1/3
Side 2: -2
Side 3: 1/3
Side 4: -2.
Complete Question:
The following set of four ordered pairs below defines the vertices, in counterclockwise order, of a quadrilateral (four-sided figure).
{(0,−5),(6,−3),(4,1),(−2,−1)
Find the slopes of the indicated sides of the quadrilateral. Simplify your answer.