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Line A passes through the points $(10,6)$ and $(2,15)$ . Line B passes through the points $(5,9)$ and $(14,-1)$ . Which statement is true? $\newline$ Choices: $\newline$ (A) Line A does not intersect line B. $\newline$ (B) Line A intersects line B at exactly one point. $\newline$ (C) Line A overlaps line B.

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Slopes of parallel and perpendicular lines

Full solution

Q. Line A passes through the points

(10,6)

and

(2,15)

. Line B passes through the points

(5,9)

and

(14,-1)

. Which statement is true?

\newline

Choices:

\newline

(A) Line A does not intersect line B.

\newline

(B) Line A intersects line B at exactly one point.

\newline

(C) Line A overlaps line B.

Calculate slope Line A: Calculate the slope of Line A using the formula $(y_2 - y_1) / (x_2 - x_1)$ where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line. For Line A, points are $(10, 6)$ and $(2, 15)$ .
Calculate slope Line B: Calculate the slope of Line B using the same formula. Points for Line B are $(5, 9)$ and $(14, -1)$ .
Compare slopes Line A and Line B: Compare the slopes of Line $A$ and Line $B$ to determine if they are parallel, the same, or neither.
Determine intersection point: Since the slopes are different, the lines must intersect at exactly one point.

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