The correct answer is The sum of the coordinates of each point is odd. This is because when you add the x and y coordinates of each point, you get an odd number:
* A(-1, 6): -1 + 6 = 5
* B(-3, 10): -3 + 10 = 7
* C(-5, 14): -5 + 14 = 9
The image you sent me is a multiple-choice question from Imagine Learning's Savvas Realize Geometry curriculum. The question asks: "Which best explains how you know that A(-1, 6) is on the same line as B(-3, 10) and C(-5, 14)?" The answer choices are:
* To get from A to B and from B to C, you move left 2 units and then up 4 units.
* The sum of the coordinates of each point is odd.
* All three points are in the same quadrant.
The correct answer is The sum of the coordinates of each point is odd. This is because when you add the x and y coordinates of each point, you get an odd number:
* A(-1, 6): -1 + 6 = 5
* B(-3, 10): -3 + 10 = 7
* C(-5, 14): -5 + 14 = 9
The other answer choices are incorrect because:
* To get from A to B and from B to C, you do not move left 2 units and then up 4 units.
* All three points are not in the same quadrant. Point A is in the second quadrant, point B is in the fourth quadrant, and point C is in the second quadrant.
Therefore, the sum of the coordinates of each point being odd is the best way to know that A(-1, 6), B(-3, 10), and C(-5, 14) are on the same line.