University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

224

Pages:

4
Author:

usarilearlyzs7g

Equations of Parallel and Perpendicular Lines (Day 1) Vocabulary Directed Line Segment: Is a line that connects two points using the shortest path. A diagram with two points labeled A and B is shown, with a line segment connecting them. 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. Diagram: Two parallel lines with equations y = -3x + 12 and y = -3x + 16 are shown. Slopes are calculated for both lines, showing they are equal. 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. Diagram: Two perpendicular lines with equations y = 2x - 1 and y = -1/2x + 7 are shown. Slopes are calculated for both lines, and their product is shown to be -1. Instructions: In Exercises 1 and 2, find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. 1 1. A(-2, 7), B(-4, 1); 3 to 1 (4 total parts) Find slope: (7 - 1) / (-2 - (-4)) = 6/2 = 3 Find the Length from P to A: 3/4 Divide the slope by the unit length: 6/4 = 3/2 = 1.5 is Δy 2/4 = 1/2 = 0.5 is Δx Add it together: (-2 - 1.5, 7 - 4.5) = P(-3.5, 2.5) 2. A(3, 1), B(8, -2); 2 to 3 (5 total parts) Find slope: (1 - (-2)) / (3 - 8) = 3/(-5) = -3/5 Find the Length from P to A: 2/5 Divide the slope by the unit length: -3/5 * 2/5 = -6/25 = -0.24 is Δy 5 * 2/5 = 2 is Δx Add it together: (3 + 2, 1 - 0.24) = P(5, -0.24)