Which set of points are collinear? Select each correct answer. ? H, A, and S ? P, H, and A ? H, D, and S ? Y, D, and T
The Correct Answer and Explanation is:
The correct answers are:
- H, A, and S
- H, D, and S
- Y, D, and T
In geometry, the term “collinear” refers to a set of points that all lie on the same single straight line. To solve this problem, we need to examine the provided diagram and determine which of the given sets of points meet this criterion.
The image displays two straight lines that intersect. One line is oriented horizontally, and the other is oriented vertically. Several points are located on these lines.
Let’s evaluate each option:
- H, A, and S: If we look at the horizontal line, we can clearly see that point H, point A, and point S are all located on this same line. Since a single straight line passes through all three points, they are collinear. This is a correct answer.
- P, H, and A: Point P is on the vertical line, while points H and A are on the horizontal line. You cannot draw a single straight line that passes through all three of these points. They form the vertices of a triangle, not a line. Therefore, this set of points is not collinear.
- H, D, and S: Point H and point S are on the horizontal line. Point D is the intersection of the two lines, which means it lies on both the horizontal and the vertical line. Since H, D, and S are all on the horizontal line, they are collinear. This is a correct answer.
- Y, D, and T: Looking at the vertical line, we can see point Y, point D, and point T. All three of these points are situated on this single vertical line. Because they all fall on the same straight path, they are collinear. This is also a correct answer.
In summary, three of the four options represent sets of collinear points because all points within those sets lie on one of the two straight lines shown in the diagram.
