Possible Intersection of Straight Lines

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Presentation transcript:

Possible Intersection of Straight Lines

Then, how can I find the coordinates of their intersection? Given two non-parallel lines L1 and L2, they must intersect. Then, how can I find the coordinates of their intersection?

Consider the following two straight lines. L1: x + y - 4 = 0 ……(1) L2: x - y - 2 = 0 ……(2) If (x0, y0) is the intersection of L1 and L2, then L1 L2 O y x (x0, y0) satisfies both equations of L1 and L2. (x0, y0) lies on  both L1 and L2. (x0, y0)

Consider the following two straight lines. L1: x + y - 4 = 0 ……(1) L2: x - y - 2 = 0 ……(2) Since the coordinates of the intersection satisfies both equations of L1 and L2, we can solve to find the coordinates of the intersection.

Consider the following two straight lines. L1: x + y - 4 = 0 ……(1) L2: x - y - 2 = 0 ……(2) (1) + (2): 2x - 6 = 0 x = 3 By substituting x = 3 into (1), we have 3 + y - 4 = 0 y = 1 ∴ L1 and L2 intersect at (3, 1).

Number of intersections of two straight lines Case 1 Case 2 Case 3 Condition unequal slopes equal slope and unequal y-intercepts equal slope and equal y-intercept No. of intersections one intersection no intersections an infinite no. of intersections

Follow-up question Determine the number of intersections between the two straight lines L1 : 3x + 2y - 5 = 0 and L2 : 6x + 2y - 3 = 0. Slope of L1 = - 2 3  For a straight line Ax + By + C = 0, Slope of L2 = = - 2 6 ∵ Slope of L1  slope of L2 ∴ L1 and L2 have one intersection.