Question

select the correct answer. 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)

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). An undefined slope occurs when the denominator \( x_2 - x_1 = 0 \) (vertical line), i.e., \( x_1 = x_2 \).

Step2: Check each option

• Option A: \((-1,1)\) and \((1,-1)\). \( x_1=-1, x_2 = 1 \). \( x_2 - x_1=1 - (-1)=2

eq0 \). Slope is defined.

• Option B: \((-2,2)\) and \((2,2)\). \( x_1=-2, x_2 = 2 \). \( x_2 - x_1=2 - (-2)=4

eq0 \). Slope is \( \frac{2 - 2}{4}=0 \) (horizontal line), defined.

• Option C: \((-3,-3)\) and \((-3,3)\). \( x_1=-3, x_2=-3 \). \( x_2 - x_1=-3 - (-3)=0 \). Denominator is 0, slope is undefined.
• Option D: \((-4,-4)\) and \((4,4)\). \( x_1=-4, x_2 = 4 \). \( x_2 - x_1=4 - (-4)=8

eq0 \). Slope is \( \frac{4 - (-4)}{8}=1 \), defined.

Answer:

C. \((-3,-3)\) and \((-3,3)\)