University:
High School
Course:
High School Geometry
Academic year:

2020
Views:

500

Pages:

3
Author:

Jamir Fox

Theorems Theorem 3.13 Slopes of Parallel Lines In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. Theorem 3.14 Slopes of Perpendicular Lines In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Horizontal lines are perpendicular to vertical lines. Exploration: Writing Equations of Parallel Lines Writing an equation of the line that is parallel to the given line and passes through the given point. a. Write an equation of the line that is parallel to the line y = 3x + 2 and passes through the point (1, -2) * Slope = 3 * Point-Slope Form: y - y₁ = m(x - x₁) * y - (-2) = 3(x - 1) * y + 2 = 3x - 3 * y = 3x - 5 3. Determine which of the lines are parallel and which of the lines are perpendicular. Line r: (4, 1), (2, 1) Slope = (1 - 1) / (4 - 2) = 0 / 2 = 0 Line s: (1, 2), (2, 1) Slope = (2 - 1) / (1 - 2) = 1 / -1 = -1 Line t: (-1, -4), (4, 0) Slope = (-4 - 0) / (-1 - 4) = -4 / -5 = 4/5 Line p: (-2, 1), (-1, -4) Slope = (1 - (-4)) / (-2 - (-1)) = 5 / -1 = -5 Line q: (3, 0), (0, 4) Slope = (0 - 4) / (3 - 0) = -4 / 3 = -4/3 So r || t (same slope of 0) p || q (same slope of -5) r ⊥ p and s ⊥ p (have reciprocal slopes) r ⊥ q and s ⊥ q (same reason) 4. Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. Line 1: (2, 0), (-2, 2) 1 Slope 1 = (0 - 2) / (2 - (-2)) = -2 / 4 = -½ Line 2: (1, -2), (4, 4) Slope 2 = (-2 - 4) / (1 - 4) = -6 / -3 = 2 Don't Graph!!! These are reciprocals So line 1 ⊥ line 2 3.5 Write an equation of the line that passes through the given point. 5. through point P(3, -2) that is parallel to [y = \frac{2}{3}x - 1] [y - (-2) = \frac{2}{3}(x - 3)] [\frac{2}{3}x] [y + 2 = \frac{2}{3}x - 2] [y = \frac{2}{3}x - 4] 6. through point P(-2, 2) that is perpendicular to [y = 2x + 3] [(y - 2) = -\frac{1}{2}(x - (-2))] [-\frac{1}{2}x] [y - 2 = -\frac{1}{2}x - 1] [y + 2 = -\frac{1}{2}x + 1] Perpendicular through the point indicated. b. [y - 1 = -\frac{2}{3}(x - 0)] coordinate plane with a line passing through (0, 1) [y - 1 = -\frac{2}{3}x] [y = -\frac{2}{3}x + 1] d. [y - (-3) = -\frac{1}{2}(x - 2)] coordinate plane with a line passing through (2, 3) [-2x - 2(-2)] [y + 3 = -2x + 4] [y = -2x + 1]