Question
he vertices of a rectangle are located at L(18, -1), M(-18, -1), N(-18, 28), and O(18, 28). What is the length of the sides LM and MN respectively?
Answers
GPT-4o mini
To find the lengths of the sides LM and MN of the rectangle formed by the vertices L(18, -1), M(-18, -1), N(-18, 28), and O(18, 28), we need to calculate the distances between the points.
1. **Calculating the length of side LM:**
- Points L and M are L(18, -1) and M(-18, -1).
- These points have the same y-coordinate (-1).
- To find the distance between them, we calculate the difference in their x-coordinates:
\[
\text{Length of LM} = |x_2 - x_1| = |-18 - 18| = |-36| = 36
\]
2. **Calculating the length of side MN:**
- Points M and N are M(-18, -1) and N(-18, 28).
- These points have the same x-coordinate (-18).
- To find the distance between them, we calculate the difference in their y-coordinates:
\[
\text{Length of MN} = |y_2 - y_1| = |28 - (-1)| = |28 + 1| = |29| = 29
\]
Therefore, the lengths of the sides are:
- Length of LM = 36
- Length of MN = 29
Thus, \(LM = 36\) and \(MN = 29\).
1. **Calculating the length of side LM:**
- Points L and M are L(18, -1) and M(-18, -1).
- These points have the same y-coordinate (-1).
- To find the distance between them, we calculate the difference in their x-coordinates:
\[
\text{Length of LM} = |x_2 - x_1| = |-18 - 18| = |-36| = 36
\]
2. **Calculating the length of side MN:**
- Points M and N are M(-18, -1) and N(-18, 28).
- These points have the same x-coordinate (-18).
- To find the distance between them, we calculate the difference in their y-coordinates:
\[
\text{Length of MN} = |y_2 - y_1| = |28 - (-1)| = |28 + 1| = |29| = 29
\]
Therefore, the lengths of the sides are:
- Length of LM = 36
- Length of MN = 29
Thus, \(LM = 36\) and \(MN = 29\).