On a map of the city, 8th Street is a line segment from point (1,4) to point (6,9). J Street is a line segment that starts at (4,–14) and stops at (–5,4). If the city council extends 8th Street in a straight line, where will it intersect J Street?

Question

20-05-2017
Mathematics

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On a map of the city, 8th Street is a line segment from point (1,4) to point (6,9). J Street is a line segment that starts at (4,–14) and stops at (–5,4). If the city council extends 8th Street in a straight line, where will it intersect J Street?

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The intersection of 8th street and J street can be determined by setting up an equation for each line segment given the points mentioned above. Note that the equation of a line can be obtained from two points such that:

y - y1 = m(x-x1), where m = (y2-y1)/(x2-x1)

For instance, the equation for 8th street is given by: y - 4 = [(9-4)/(6-1)]*(x-1). On the other hand, the equation for J street is given by: y + 14 = [(4+14)/(-5-4)]*(x-4). Simplifying the 2 equations we get: Eqn. (1) y = x + 3 and Eqn. (2) y = -2x - 6

Solving the 2 equations simultaneously, we obtain x = -3, y = 0. Thus, if the city council extends 8th street in a straight line, it will intersect J street at (-3,0).