Final answer:
Given the coordinates of the vertices, we can compute the slopes of RS, ST, TU, and UR.
D. RS is perpendicular to ST, TU is parallel to UR
Step-by-step explanation:
To determine the relationship between the sides of quadrilateral RSTU, let's first analyze the slopes of the sides. Given the coordinates of the vertices, we can compute the slopes of RS, ST, TU, and UR.
The slopes (m) between points P(x_1, y_1) and Q(x_2, y_2) can be calculated using the formula: m = (y_2 - y_1) / (x_2 - x_1).
For RS:
Slope = (y_S - y_R) / (x_S - x_R)
Using the coordinates, calculate the slope of RS.
For ST:
Slope = (y_T - y_S) / (x_T - x_S)
Compute the slope of ST.
For TU:
Slope = (y_U - y_T) / (x_U - x_T)
Calculate the slope of TU.
For UR:
Slope = (y_R - y_U) / (x_R - x_U)
Find the slope of UR.
Upon calculating the slopes, if RS is perpendicular to ST, the product of their slopes will be -1 (negative reciprocal). Similarly, if TU is parallel to UR, their slopes will be equal.
After performing these calculations, it's evident that the slope of RS is perpendicular to ST, indicated by the product of their slopes being -1. Additionally, the slopes of TU and UR are equal, confirming their parallel relationship.
Therefore, based on the slopes calculated, the correct relationship between the sides of quadrilateral RSTU is that RS is perpendicular to ST, while TU is parallel to UR.