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 create the side. Slope of side RS= Slope of side ST= 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.

A) RS and TU are parallel, ST and UR are perpendicular
B) RS and ST are parallel, TU and UR are perpendicular
C) RS and UR are parallel, ST and TU are perpendicular
D) RS and TU are perpendicular, ST and UR are parallel

Answer 1

By calculating the slopes of each side of quadrilateral RSTU, it was determined that sides RS and UR are parallel, as well as sides ST and TU, confirming option C as the correct answer.

Step-by-step explanation:

To determine which sides of quadrilateral RSTU are parallel or perpendicular, we need to find the slope of each side. By graphing the coordinates R(-1, 1), S(1, -2), T(5, 0), and U(3, 3), we can use these points to calculate the slopes.

The slope of a line segment can be found using the formula (y2 - y1)/(x2 - x1). Let's calculate the slope for each side:

• Slope of RS = (-2 - 1)/(1 - (-1)) = -3/2
• Slope of ST = (0 - (-2))/(5 - 1) = 2/4 = 1/2
• Slope of TU = (3 - 0)/(3 - 5) = 3/(-2) = -3/2
• Slope of UR = (3 - 1)/(3 - (-1)) = 2/4 = 1/2

Since RS and TU have the same slope of -3/2, they are parallel. Similarly, ST and UR have the same slope of 1/2, indicating they are also parallel. There are no slopes that represent a negative reciprocal of each other, which would indicate perpendicular sides. Therefore, the correct answer is C) RS and UR are parallel, ST and TU are perpendicular.