Question

Which best explains how you know that A(-1, 6) is on the same line as B(-3, 10)

and C(-5, 14)?
To get from A to B and from B to C, you move left 2 units
and then up 4 units.
The points are named with three consecutive letters of the
alphabet.
The sum of the coordinates of each point is odd.
All three points are in the same quadrant.

Answer 1

Points A(-1, 6), B(-3, 10), and C(-5, 14) are on the same line because they have the same slope, which indicates a constant rate of change in the x- and y-coordinates, thus proving collinearity.

Step-by-step explanation:

The best explanation for how we know that points A(-1, 6), B(-3, 10), and C(-5, 14) are on the same line is by looking at the pattern of their coordinates. When we move from A to B, we go 2 units to the left (x-coordinate decreases by 2) and 4 units up (y-coordinate increases by 4). The same pattern is observed when moving from B to C. This consistent change in coordinates indicates that they lie on the same straight line, which can be determined by the slope formula, Δy/Δx. Since the change in y over the change in x is constant, the points share the same slope and are therefore collinear.

To further confirm, let's calculate the slope between A and B, which is (10 - 6) / (-3 - (-1)) = 4 / -2 = -2. The slope between B and C is (14 - 10) / (-5 - (-3)) = 4 / -2 = -2. The slopes are equal, confirming that A, B, and C are on the same line.