Question

find the perimeter of the polygon with the vertices q(-3, 2), r(1, 2), s(1, -2), and t(-3, -2). the perimeter is □ units.

Explanation:

Step1: Identify the shape

The vertices are \( Q(-3, 2) \), \( R(1, 2) \), \( S(1, -2) \), and \( T(-3, -2) \). Let's check the distances between consecutive points.

Step2: Calculate \( QR \)

For \( Q(-3, 2) \) and \( R(1, 2) \), since the \( y \)-coordinates are the same, the distance is the difference in \( x \)-coordinates. So \( QR = |1 - (-3)| = |4| = 4 \).

Step3: Calculate \( RS \)

For \( R(1, 2) \) and \( S(1, -2) \), the \( x \)-coordinates are the same, so the distance is the difference in \( y \)-coordinates. \( RS = |-2 - 2| = |-4| = 4 \).

Step4: Calculate \( ST \)

For \( S(1, -2) \) and \( T(-3, -2) \), \( y \)-coordinates are the same. Distance is \( |-3 - 1| = |-4| = 4 \).

Step5: Calculate \( TQ \)

For \( T(-3, -2) \) and \( Q(-3, 2) \), \( x \)-coordinates are the same. Distance is \( |2 - (-2)| = |4| = 4 \).

Step6: Calculate perimeter

Perimeter is the sum of all sides: \( 4 + 4 + 4 + 4 = 16 \).

Answer:

16