Question

28 The vertices of a quadrilateral are listed below. Q(-5,7),R(8,7),S(6,-6),T(-7,-6) Which of the following is the strongest classification that identifies this auadrilateral?

Answer 1

The strongest classification for the quadrilateral with vertices Q(-5,7), R(8,7), S(6,-6), and T(-7,-6) is B. The quadrilateral is a parallelogram.

Detailed Calculation Steps:

1. Calculate side lengths using the distance formula for each pair of vertices that form sides:

- QR = RS = ST = TQ (all sides have the same length).

2. Calculate slopes of each side to determine parallelism:

- Slope of QR and ST is 0, indicating they are horizontal and parallel.

- Slope of RS and TQ is \( \frac{13}{2} \), indicating they are parallel.

3. Determine right angles by checking perpendicular slopes:

- The slopes of QR and RS, as well as ST and TQ, are not negative reciprocals of each other, so they are not perpendicular.

4. Check for equal diagonals (which would indicate a rectangle or square):

- The diagonals QS and RT are not equal in length.

Since opposite sides are equal and parallel, but there are no right angles or equal diagonals, the quadrilateral is classified as a parallelogram.

the complete Question is given below:

The vertices of a quadrilateral are listed below. Q(-5,7), R(8,7), S(6,-6), T(-7,-6) Which of the following is the strongest classification that identifies this quadrilateral? A. The quadrilateral is a rectangle. B. The quadrilateral is a parallelogram.. C. The quadrilateral is a rhombus.. D. The quadrilateral is a square.

Answer 2

The strongest classification for the quadrilateral with vertices Q(-5,7), R(8,7), S(6,-6), and T(-7,-6) is B. The quadrilateral is a parallelogram.

Opposite sides are equal in length: We can calculate the side lengths using the distance formula:

QR = √((8 - (-5))^2 + (7 - 7)^2) = 13

RS = √((6 - 8)^2 + (-6 - 7)^2) = 13

ST = √((-7 - 6)^2 + (-6 - (-6))^2) = 13

TQ = √((-7 - (-5))^2 + (-6 - 7)^2) = 13

Therefore, opposite sides QR and ST, as well as RS and TQ, have the same length, satisfying the condition for a parallelogram.

Not all sides are equal: While opposite sides are equal, the adjacent sides are not: QR is not equal to RS, and ST is not equal to TQ. This eliminates options C (rhombus) and D (square), which require all sides to be equal.

Right angles not guaranteed: We cannot determine whether the angles of the quadrilateral are right angles just from the side lengths. Therefore, option A (rectangle) is also not confirmed.

Therefore, based on the given information, classifying the quadrilateral as a parallelogram is the most accurate and specific option. It captures the key property of opposite sides being equal without making any unwarranted assumptions about other characteristics like angles or side lengths being equal.

Complete Question:

The vertices of a quadrilateral are listed below.
Q(-5,7), R(8,7), S(6,-6), T(-7,-6)
Which of the following is the strongest classification that identifies this quadrilateral?

A. The quadrilateral is a rectangle.

B. The quadrilateral is a parallelogram.

C. The quadrilateral is a rhombus.

D. The quadrilateral is a square.