Question

Which two points have an undefined slope?

A.
(-1,1) and (1,-1)
B.
(-2,2) and (2,2)
C.
(-3,-3) and (-3,3)
D.
(-4,-4) and (4,4)

Answer 1

The slope of a line is defined as the change in the y-coordinates divided by the change in the x-coordinates (rise over run). A slope is considered undefined when the change in the x-coordinates (denominator) is zero, which occurs when the two points have the same x-coordinate.

Let's evaluate each option:

A. Points (-1,1) and (1,-1):
- x-coordinates: -1 and 1 (change in x ≠ 0) → slope is defined.

B. Points (-2,2) and (2,2):
- x-coordinates: -2 and 2 (change in x ≠ 0) → slope is defined.

C. Points (-3,-3) and (-3,3):
- x-coordinates: -3 and -3 (change in x = 0) → slope is undefined.

D. Points (-4,-4) and (4,4):
- x-coordinates: -4 and 4 (change in x ≠ 0) → slope is defined.

The two points that have an undefined slope are in option C: **(-3,-3) and (-3,3)**.