More on Parallel and Perpendicular Lines
More on Parallel and Perpendicular Lines By Ma. Louise De Las Peñas et’s look at more problems on parallel and perpendicular lines. The following results, presented Lin the article, “About Slope” will be used to solve the problems. Theorem 1. Let L1 and L2 be two distinct nonvertical lines with slopes m1 and m2, respectively. Then L1 is parallel to L2 if and only if m1 = m2. Theorem 2. Let L1 and L2 be two distinct nonvertical lines with slopes m1 and m2, respectively. Then L1 is perpendicular to L2 if and only if m1m2 = -1. Example 1. The perpendicular bisector of a segment is the line which is perpendicular to the segment at its midpoint. Find equations of the three perpendicular bisectors of the sides of a triangle with vertices at A(-4,1), B(4,5) and C(4,-3). Solution: Consider the triangle with vertices A(-4,1), B(4,5) and C(4,-3), and the midpoints E, F, G of sides AB, BC, and AC, respectively. TATSULOK FirstSecond Year Year Vol. Vol. 12 No.12 No. 1a 2a e-Pages 1 In this problem, our aim is to fi nd the equations of the lines which pass through the midpoints of the sides of the triangle and at the same time are perpendicular to the sides of the triangle. Figure 1 The fi rst step is to fi nd the midpoint of every side. The next step is to fi nd the slope of the lines containing every side. The last step is to obtain the equations of the perpendicular bisectors.
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