Question

Manuela claims that Segment A B and Segment P Q are congruent.

On a coordinate plane, segment P Q goes from (negative 3, negative 1) to (negative 3, 3) and segment A B goes from (0, 1) to (3, 1).

Which statement best describes her claim?
She is incorrect because the segments do not have the same orientation.
She is incorrect because the segments do not have the same length.
She is correct because the segments have the same length.
She is correct because the segments have the same orientation.

Answer 1

To assess Manuela's claim about the congruence of Segment AB and Segment PQ, we need to find the lengths and orientations of each segment.

1. **Length of Segment PQ**:
- The endpoints of Segment PQ are \((-3, -1)\) and \((-3, 3)\). Since the x-coordinates are the same, this segment is vertical.
- The length of Segment PQ can be calculated as the difference in the y-coordinates:
\[
\text{Length of PQ} = |3 - (-1)| = |3 + 1| = 4.
\]

2. **Length of Segment AB**:
- The endpoints of Segment AB are \((0, 1)\) and \((3, 1)\). Since the y-coordinates are the same, this segment is horizontal.
- The length of Segment AB can be calculated as the difference in the x-coordinates:
\[
\text{Length of AB} = |3 - 0| = 3.
\]

Now let's analyze Manuela's claim regarding congruence:

- The lengths of the two segments are different (4 for Segment PQ and 3 for Segment AB), which means they cannot be congruent.
- Furthermore, the segments have different orientations; Segment PQ is vertical, while Segment AB is horizontal.

Given that the lengths are not the same, the correct statement about her claim is:

**She is incorrect because the segments do not have the same length.**