Question

determine the perimeter of the given figure on the coordinate plane. round your answer to the nearest hundredth, if necessary. figure pqrst > enter the answer in the space provided. use numbers instead of words. units

Explanation:

Step1: Identify side - lengths

Assume grid squares are 1 unit each. Count horizontal and vertical side - lengths directly. For non - horizontal/vertical sides, use the Pythagorean theorem. Let's assume coordinates: \(P(-8,5)\), \(Q(-4,8)\), \(R(-2,6)\), \(S(-2,3)\), \(T(-8,3)\).

Step2: Calculate \(PQ\)

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(P(-8,5)\) and \(Q(-4,8)\), \(x_1=-8,y_1 = 5,x_2=-4,y_2 = 8\).
\[

$$\begin{align*} PQ&=\sqrt{(-4+8)^2+(8 - 5)^2}\\ &=\sqrt{4^2+3^2}\\ &=\sqrt{16 + 9}\\ &=\sqrt{25}\\ &=5 \end{align*}$$

\]

Step3: Calculate \(QR\)

For \(Q(-4,8)\) and \(R(-2,6)\), \(x_1=-4,y_1 = 8,x_2=-2,y_2 = 6\)
\[

$$\begin{align*} QR&=\sqrt{(-2 + 4)^2+(6 - 8)^2}\\ &=\sqrt{2^2+( - 2)^2}\\ &=\sqrt{4+4}\\ &=\sqrt{8}\\ &\approx2.83 \end{align*}$$

\]

Step4: Calculate \(RS\)

\(R(-2,6)\) and \(S(-2,3)\) are vertical, so \(RS=|6 - 3| = 3\)

Step5: Calculate \(ST\)

\(S(-2,3)\) and \(T(-8,3)\) are horizontal, so \(ST=|-2+8| = 6\)

Step6: Calculate \(TP\)

\(T(-8,3)\) and \(P(-8,5)\) are vertical, so \(TP=|5 - 3| = 2\)

Step7: Calculate perimeter

Perimeter \(=PQ + QR+RS+ST+TP\)
\[

$$\begin{align*} &=5+2.83 + 3+6+2\\ &=18.83 \end{align*}$$

\]

Answer:

18.83