Final answer:
Options a) (1,3), (-1,3) and c) (-4,-3), (4, -3) both have pairs of points with the same y-coordinate and different x-coordinates, which defines a line segment parallel to the x-axis.
Step-by-step explanation:
To determine which pair of points defines a line segment parallel to the x-axis, we need to find the pair where the y-coordinates are the same, because a line parallel to the x-axis varies in the x-coordinate but is constant in the y-coordinate.
Looking at each option:
- Option a) (1,3), (-1,3) - both points have the y-coordinate of 3.
- Option b) (4,3), (4, -3) - the x-coordinates are the same, not the y-coordinates, indicating a line parallel to the y-axis.
- Option c) (-4,-3), (4, -3) - both points have the y-coordinate of -3.
- Option d) (3, 4), (-3,-4) - both the x-coordinate and y-coordinate differ.
Options a) and c) both define line segments parallel to the x-axis because their y-coordinates are the same although their x-coordinates differ.