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Line $A$ passes through the points $(-3,13)$ and $(0,-5)$ . Line $B$ passes through the points $(5,-6)$ and $(-10,12)$ . $\newline$ Which statement is true? $\newline$ Choices: $\newline$ (A) Line $A$ does not intersect line $B$ . $\newline$ (B) Line $A$ overlaps line $B$ . $\newline$ (C) Line $A$ intersects line $B$ at exactly one point.

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Slopes of parallel and perpendicular lines

Full solution

Q. Line

A

passes through the points

(-3,13)

and

(0,-5)

. Line

B

passes through the points

(5,-6)

and

(-10,12)

.

\newline

Which statement is true?

\newline

Choices:

\newline

(A) Line

A

does not intersect line

B

.

\newline

(B) Line

A

overlaps line

B

.

\newline

(C) Line

A

intersects line

B

at exactly one point.

Calculate Slope Line A: Calculate the slope of Line A using the points $(-3,13)$ and $(0,-5)$ . $\newline$ Slope formula: $\frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ Slope of Line A = $\frac{-5 - 13}{0 + 3} = \frac{-18}{3} = -6$
Calculate Slope Line B: Calculate the slope of Line B using the points $(5,-6)$ and $(-10,12)$ . $\newline$ Slope formula: $\frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ Slope of Line B = $\frac{12 + 6}{-10 - 5} = \frac{18}{-15} = -\frac{6}{5}$
Compare Slopes: Compare the slopes of Line A and Line B. $\newline$ Slope of Line A = $-6$ , Slope of Line B = $-\frac{6}{5}$ $\newline$ Since the slopes are different, the lines are not parallel and must intersect at exactly one point.

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