Question

question 6 (multiple choice worth 1 points) (04.03 mc) find the perimeter of the polygon. round your answer to the nearest tenth. 37 38 39 40

Explanation:

Answer:

First, we find the coordinates of each vertex:

• \( P(-1, 11) \)
• \( Q(-4, 5) \)
• \( R(2, 0) \)
• \( S(1, 7) \)
• \( T(8, 7) \)

Now, we calculate the distance between each consecutive pair of vertices using the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \):

1. Distance \( PQ \):

\( x_1 = -1, y_1 = 11 \); \( x_2 = -4, y_2 = 5 \)
\( d_{PQ} = \sqrt{(-4 - (-1))^2 + (5 - 11)^2} = \sqrt{(-3)^2 + (-6)^2} = \sqrt{9 + 36} = \sqrt{45} \approx 6.7 \)

1. Distance \( QR \):

\( x_1 = -4, y_1 = 5 \); \( x_2 = 2, y_2 = 0 \)
\( d_{QR} = \sqrt{(2 - (-4))^2 + (0 - 5)^2} = \sqrt{(6)^2 + (-5)^2} = \sqrt{36 + 25} = \sqrt{61} \approx 7.8 \)

1. Distance \( RS \):

\( x_1 = 2, y_1 = 0 \); \( x_2 = 1, y_2 = 7 \)
\( d_{RS} = \sqrt{(1 - 2)^2 + (7 - 0)^2} = \sqrt{(-1)^2 + (7)^2} = \sqrt{1 + 49} = \sqrt{50} \approx 7.1 \)

1. Distance \( ST \):

\( x_1 = 1, y_1 = 7 \); \( x_2 = 8, y_2 = 7 \)
\( d_{ST} = \sqrt{(8 - 1)^2 + (7 - 7)^2} = \sqrt{(7)^2 + 0^2} = \sqrt{49} = 7 \)

1. Distance \( TP \):

\( x_1 = 8, y_1 = 7 \); \( x_2 = -1, y_2 = 11 \)
\( d_{TP} = \sqrt{(-1 - 8)^2 + (11 - 7)^2} = \sqrt{(-9)^2 + (4)^2} = \sqrt{81 + 16} = \sqrt{97} \approx 9.8 \)

Now, we sum up all these distances to find the perimeter:
\( \text{Perimeter} \approx 6.7 + 7.8 + 7.1 + 7 + 9.8 = 38.4 \approx 38 \) (rounded to the nearest tenth)

So the answer is 38.