Question

Given quadrilateral RSTU, follow the steps to tell which sides (if any) are parallel and which are perpendicular for the

coordinates of the vertices.
R(-1, 1), S(1,-2), T(5,0), U(3, 3)
Part 1
Graph the coordinates of quadrilateral RSTU on a coordinate plane. Assign the appropriate variables to the coordinates.
Part 2
Find the slope of each side of the RSTU, using the two points that creates the side.
Slope of side RS=
Slope of side STE
Slope of side TU
Slope of side UR=
Part 3
Use the slope of each side to name the pairs of parallel and perpendicular sides. For each relationship between a pair
of sides, explain in complete sentences, why the relationship between the sides exists.
Complete your work in the space provided or upload a file that can display math symbols if your work requires it

Answer 1

Quadrilateral RSTU is graphed on a coordinate plane, and the slopes of each side are calculated. Based on the slopes, we determine the pairs of parallel and perpendicular sides.

Step-by-step explanation:

Part 1

To graph quadrilateral RSTU, we plot the given coordinates on a coordinate plane. R(-1, 1), S(1,-2), T(5,0), and U(3, 3).

Note: The x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position.

Graph:

Part 2

To find the slope of each side, we use the formula:

Slope = (change in y-coordinates)/(change in x-coordinates)

Slope of RS = (y2-y1)/(x2-x1) = (-2-1)/(1-(-1)) = -3/2

Slope of ST = (y2-y1)/(x2-x1) = (0-(-2))/(5-1) = 2/4 = 1/2

Slope of TU = (y2-y1)/(x2-x1) = (3-0)/(3-5) = 3/-2 = -3/2

Slope of UR = (y2-y1)/(x2-x1) = (3-1)/(3-(-1)) = 2/4 = 1/2

Part 3

Using the slopes, we can determine the pairs of parallel and perpendicular sides:

Pairs of parallel sides:
RS and TU
ST and UR

Pairs of perpendicular sides:
RS and ST
TU and UR

Step-by-step explanation:
The relationship between parallel sides exists because parallel lines have equal slopes. In this case, RS and TU have slopes of -3/2, while ST and UR both have slopes of 1/2.
The relationship between perpendicular sides exists because perpendicular lines have slopes that are negative reciprocals. In this case, RS and ST have slopes of -3/2 and 1/2, respectively. TU and UR also have slopes of -3/2 and 1/2, respectively, making them perpendicular.