Line A passes through the points (-3,13) and (0,-5). Line B passes through the points (5,-6) and (-10,12). Which statement is true? Choices: (A)Line A does not intersect line B. (B)Line A overlaps line B. (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). Slope formula: (y2 - y1) / (x2 - x1) Slope of Line A = (-5 - 13) / (0 + 3) = -18 / 3 = -6 Calculate Slope Line B: Calculate the slope of Line B using the points (5,-6) and (-10,12). Slope formula: (y2 - y1) / (x2 - x1) Slope of Line B = (12 + 6) / (-10 - 5) = 18 / -15 = -6/5 Compare Slopes: Compare the slopes of Line A and Line B. Slope of Line A = -6, Slope of Line B = -6/5 Since the slopes are different, the lines are not parallel and must intersect at exactly one point.

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Math Problems

Grade 8

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

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.