Question

identify the figure with the vertices q(-3,2), r(1,2), s(1,-4), and t(-3,-4). select choice

Explanation:

Step1: Analyze coordinates of Q and R

Points \( Q(-3,2) \) and \( R(1,2) \) have the same \( y \)-coordinate. The distance \( QR \) is \( |1 - (-3)| = 4 \) (horizontal distance, since \( y \)-coordinates are equal).

Step2: Analyze coordinates of R and S

Points \( R(1,2) \) and \( S(1,-4) \) have the same \( x \)-coordinate. The distance \( RS \) is \( |-4 - 2| = 6 \) (vertical distance, since \( x \)-coordinates are equal).

Step3: Analyze coordinates of S and T

Points \( S(1,-4) \) and \( T(-3,-4) \) have the same \( y \)-coordinate. The distance \( ST \) is \( |-3 - 1| = 4 \) (horizontal distance, same as \( QR \)).

Step4: Analyze coordinates of T and Q

Points \( T(-3,-4) \) and \( Q(-3,2) \) have the same \( x \)-coordinate. The distance \( TQ \) is \( |2 - (-4)| = 6 \) (vertical distance, same as \( RS \)).

Step5: Determine the shape

Since opposite sides are equal and all angles are right angles (because adjacent sides are horizontal and vertical, so they are perpendicular), the figure is a rectangle.

Answer:

The figure with vertices \( Q(-3,2) \), \( R(1,2) \), \( S(1,-4) \), and \( T(-3,-4) \) is a rectangle.