Which of the following is true of (1, 4) and (1, -7)?
The points lie on a vertical line.
The points lie on a diagonal line.
More information is needed to determine the relationship between the two points.
The points lie on a horizontal line.
Answer (1)
The points lie on a vertical line.
Explanation
Analyze the problem We are given two points, (1, 4) and (1, -7), and we need to determine their relationship. The options are that they lie on a vertical line, a horizontal line, a diagonal line, or that more information is needed.
Examine the coordinates Let's examine the coordinates of the points. The x-coordinate of both points is 1. This means that the points have the same x-coordinate, which indicates that they lie on a vertical line.
Calculate the slope To further confirm, we can calculate the slope between the two points. The slope, m , is given by the formula: m = x 2 − x 1 y 2 − y 1 Substituting the coordinates of the points (1, 4) and (1, -7), we get: m = 1 − 1 − 7 − 4 = 0 − 11 Since division by zero is undefined, the slope is undefined, which confirms that the line is vertical.
Conclusion Therefore, the points (1, 4) and (1, -7) lie on a vertical line.
Examples
Imagine you're designing a building and need to place two support beams on the same vertical line for structural integrity. If one beam is at coordinates (1, 4) and the other at (1, -7) on your blueprint, you know they are aligned vertically, ensuring they share the same x-coordinate. This concept is crucial in architecture and engineering for maintaining balance and stability in structures.
