Question

1. find the area of rectangle jklm round to the nearest tenth if necessary. j(-4, 4), k(6, 0), l(14, -5), m(-6, -1)

Explanation:

Step1: Find length of JK

Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For $J(-4, 4)$ and $K(6, 0)$:
$d_{JK} = \sqrt{(6 - (-4))^2 + (0 - 4)^2} = \sqrt{(10)^2 + (-4)^2} = \sqrt{100 + 16} = \sqrt{116} \approx 10.77$

Step2: Find length of KL

For $K(6, 0)$ and $L(14, -5)$:
$d_{KL} = \sqrt{(14 - 6)^2 + (-5 - 0)^2} = \sqrt{(8)^2 + (-5)^2} = \sqrt{64 + 25} = \sqrt{89} \approx 9.43$

Step3: Calculate area of rectangle

Area of rectangle is $length \times width$. So area $= 10.77 \times 9.43 \approx 101.6$ (or use exact values: $\sqrt{116} \times \sqrt{89} = \sqrt{116 \times 89} = \sqrt{10324} = 101.6$ when rounded to nearest tenth)

Answer:

101.6