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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. [tex]\((-4,-4)\)[/tex] and [tex]\((4,4)\)[/tex]



Answer :

GinnyAnswer
To determine which two points have an undefined slope, we need to understand what it means for a slope to be undefined. The slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

The slope is undefined when the denominator \(x_2 - x_1\) is zero, which happens when \(x_2 = x_1\). This means that the line is vertical.

Let's examine each of the given pairs of points:

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

Since \(x_2 - x_1 \neq 0\), the slope is not undefined.

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

Since \(x_2 - x_1 \neq 0\), the slope is not undefined.

Option C: \((-3,-3)\) and \((-3,3)\)
- \(x_1 = -3\)
- \(x_2 = -3\)
- \(x_2 - x_1 = -3 - (-3) = 0\)

Since \(x_2 - x_1 = 0\), the slope is undefined.

Option D: \((-4,-4)\) and \((4,4)\)
- \(x_1 = -4\)
- \(x_2 = 4\)
- \(x_2 - x_1 = 4 - (-4) = 8\)

Since \(x_2 - x_1 \neq 0\), the slope is not undefined.

Based on the analysis, the correct answer is:
C. [tex]\((-3,-3)\)[/tex] and [tex]\((-3,3)\)[/tex]

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