Question

Find the area of the rectangle LMNO , with vertices L(−5,7) ,M(−1,7) , N(−1,−3) , and O(−5,−3) .(1 point) Responses 28 ​units2 28 units squared 8 ​units2 8 units squared 40 ​units2 40 units squared 100 ​units2

Answer 1

To find the area of the rectangle LMNO with vertices L(−5,7), M(−1,7), N(−1,−3), and O(−5,−3), we first need to determine the lengths of the sides of the rectangle.

1. **Length of the base:** The distance between points L(−5,7) and M(−1,7) can be calculated using the formula for distance between two points on a horizontal line, which is simply the difference in x-coordinates:

\[
\text{Length} = |x_2 - x_1| = |-1 - (-5)| = |-1 + 5| = |4| = 4 \text{ units}
\]

2. **Length of the height:** The distance between points L(−5,7) and O(−5,−3) can be calculated using the formula for distance between two points on a vertical line, which is the difference in y-coordinates:

\[
\text{Height} = |y_2 - y_1| = |−3 - 7| = |−10| = 10 \text{ units}
\]

3. **Area of the rectangle:** The area \(A\) of the rectangle is given by the formula:

\[
A = \text{Length} \times \text{Height} = 4 \times 10 = 40 \text{ square units}
\]

Therefore, the area of rectangle LMNO is \( \boxed{40} \) square units.