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Find the area of rectangle JKLM

with vertices J(−5,−2)
, K(−1,−2)
, L(−1,7)
, and M(−5,7)
.(1 point)

1 answer

To find the area of rectangle JKLM with the given vertices, we first identify the lengths of its sides.

  1. Calculate the length of side JK:

    • The coordinates of J are \((-5, -2)\) and K are \((-1, -2)\).
    • The length of JK can be calculated using the distance formula or by noting that both points have the same \(y\)-coordinate (meaning they are on a horizontal line): \[ \text{Length of JK} = |x_K - x_J| = |-1 - (-5)| = |-1 + 5| = |4| = 4 \]

  2. Calculate the length of side JL:

    • The coordinates of J are \((-5, -2)\) and L are \((-1, 7)\).
    • The length of JL can be calculated similarly, but here we will find the vertical length: \[ \text{Length of JL} = |y_L - y_J| = |7 - (-2)| = |7 + 2| = |9| = 9 \]

  3. Calculate the area of the rectangle:

    • The area \(A\) of a rectangle can be found by multiplying the lengths of adjacent sides: \[ A = \text{Length of JK} \times \text{Length of JL} = 4 \times 9 = 36 \]

Thus, the area of rectangle JKLM is \( \boxed{36} \).