Question

what is the perimeter of trapezoid jklm? j(-7, 4) k(-4, 4) m(-8, 3) l(-2, 3) 9 + \sqrt{2}+\sqrt{5} units 9 + 2\sqrt{2} units \sqrt{2}+\sqrt{5} units 2+\sqrt{2}+\sqrt{5} units

Explanation:

Step1: Calculate length of JK

Since J(-7,4) and K(-4,4) have the same y - coordinate, use the distance formula for points with same y - value: $d=\vert x_2 - x_1\vert$. Here $x_1=-7,x_2 = - 4$, so $JK=\vert-4-(-7)\vert=3$.

Step2: Calculate length of KL

Since L(-2,3) and K(-4,4), use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-4,y_1 = 4,x_2=-2,y_2 = 3$, so $KL=\sqrt{(-2+4)^2+(3 - 4)^2}=\sqrt{4 + 1}=\sqrt{5}$.

Step3: Calculate length of LM

Since L(-2,3) and M(-8,3) have the same y - coordinate, $LM=\vert-8-(-2)\vert=6$.

Step4: Calculate length of MJ

Since M(-8,3) and J(-7,4), use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-8,y_1 = 3,x_2=-7,y_2 = 4$, so $MJ=\sqrt{(-7 + 8)^2+(4 - 3)^2}=\sqrt{1+1}=\sqrt{2}$.

Step5: Calculate the perimeter P

$P=JK + KL+LM+MJ=3+\sqrt{5}+6+\sqrt{2}=9+\sqrt{2}+\sqrt{5}$.

Answer:

$9+\sqrt{2}+\sqrt{5}$ units