Question

The vertices of a rectangle are located at A (4, 1), B (-4, 1), C (-4, 3), and D (4, 3). What are the lengths of the sides AB and BC respectively?

Answer 1

To find the lengths of the sides AB and BC of the rectangle with vertices A(4, 1), B(-4, 1), C(-4, 3), and D(4, 3), we can calculate the distances between the relevant points.

1. **Length of side AB**:
- Points A and B are at A(4, 1) and B(-4, 1).
- The length of side AB can be calculated using the distance formula:
\[
\text{Distance} = |x_2 - x_1|
\]
- Here, \(x_1 = 4\) and \(x_2 = -4\).
\[
\text{Length of AB} = |-4 - 4| = |-8| = 8
\]

2. **Length of side BC**:
- Points B and C are at B(-4, 1) and C(-4, 3).
- The length of side BC can also be calculated using the distance formula:
\[
\text{Distance} = |y_2 - y_1|
\]
- Here, \(y_1 = 1\) and \(y_2 = 3\).
\[
\text{Length of BC} = |3 - 1| = |2| = 2
\]

Thus, the lengths of the sides are:
- Length of AB = 8
- Length of BC = 2