Question

Find the area of rectangle JKLM
with vertices J(−5,−2)
, K(−1,−2)
, L(−1,7)
, and M(−5,7)
.(1 point)

Answer 1

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 \( \boxed{36} \).