Question

#2
what is the
perimeter of the
shape?

Explanation:

Step1: Find the lengths of the sides

• Length of \(JK\): The \(y\)-coordinates of \(J(-4,4)\) and \(K(-4, - 4)\). Using the distance formula for vertical line \(d=\vert y_2 - y_1\vert\), \(d_{JK}=\vert4-(-4)\vert = 8\)
• Length of \(KL\): The \(x\)-coordinates of \(K(-4,-4)\) and \(L(3,-4)\). Using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\), \(d_{KL}=\vert3-(-4)\vert = 7\)
• Length of \(LM\): The \(y\)-coordinates of \(L(3,-4)\) and \(M(3,2)\). Using the distance formula for vertical line \(d=\vert y_2 - y_1\vert\), \(d_{LM}=\vert2-(-4)\vert = 6\)
• Length of \(MP\): The \(x\)-coordinates of \(M(3,2)\) and \(P(-1,2)\). Using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\), \(d_{MP}=\vert-1 - 3\vert=4\)
• Length of \(PJ\): The \(y\)-coordinates of \(P(-1,4)\) and \(J(-4,4)\). Using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\), \(d_{PJ}=\vert-4-(-1)\vert = 3\)

Step2: Calculate the perimeter

Perimeter \(P=d_{JK}+d_{KL}+d_{LM}+d_{MP}+d_{PJ}\)
\(P = 8 + 7+6 + 4+5\)
\(P=30\)

Answer:

1. \(30\) units