Line A passes through the points (–2,27) and (1,–9). Line B passes through the points (–1,15) and (3,–33).Which statement is true?Line A overlaps line B.Line A does not intersect line B.Line A intersects line B at exactly one point.Submit
Question
Line A passes through the points (–2,27) and (1,–9). Line B passes through the points (–1,15) and (3,–33).Which statement is true?Line A overlaps line B.Line A does not intersect line B.Line A intersects line B at exactly one point.Submit
Solution
To answer this question, we first need to find the slopes of the two lines.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1) / (x2 - x1).
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For Line A, the slope (m1) is: m1 = ( -9 - 27 ) / ( 1 - ( -2 ) ) = -36 / 3 = -12
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For Line B, the slope (m2) is: m2 = ( -33 - 15 ) / ( 3 - ( -1 ) ) = -48 / 4 = -12
Since the slopes of both lines are equal, the lines are either parallel or the same line (overlap).
To check if they are the same line, we can compare their y-intercepts. The y-intercept is found by substituting one of the points into the equation y = mx + c and solving for c.
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For Line A, using point (1, -9), the y-intercept (c1) is: c1 = -9 - ( -12 * 1 ) = -9 + 12 = 3
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For Line B, using point (3, -33), the y-intercept (c2) is: c2 = -33 - ( -12 * 3 ) = -33 + 36 = 3
Since both lines have the same slope and the same y-intercept, they are the same line. Therefore, Line A overlaps Line B.
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