Question

Consider the points (-2, 1) and (1, -1) .Which could be a third point that lies on the lines containing the original two points?

a. (-2, -1)
b. (1, 1)
c. (0, 0)
d. None

Answer 1

To determine the third point that lies on the line containing the two given points, we need to find the equation of the line using the slope-intercept form and substitute the coordinates of each choice to check if they satisfy the equation.

Step-by-step explanation:

To determine the third point that lies on the line containing the two given points, we need to find the equation of the line formed by these points. Using the slope-intercept form, we find the equation of the line passing through (-2, 1) and (1, -1) as y = -x - 1. We can substitute the x and y coordinates of each choice to see if they satisfy the equation.

a. (-2, -1): -1 = -(-2) - 1 ➡️ This is correct.

b. (1, 1): 1 ≠ -1 ➡️ This is incorrect.

c. (0, 0): 0 ≠ -1 ➡️ This is incorrect.

d. None: Since choice a satisfies the equation, the answer is a. (-2, -1).