Another way to characterize parallel lines are distinct lines with the same slope. Horizontal and vertical lines are always perpendicular: therefore, two lines, one of which has a zero slope and the other an undefined slope are perpendicular.Įxample 1: If line l has slope 3/4, then (a) any line parallel to l has slope _, and (b) any line perpendicular to l has slope _.Įxample 2: Given points Q, R, S, and T, tell which sides, if any, of quadrilateral QRST in Figure 1 are parallel or perpendicular.įigure 1 Determining which sides, if any, of a quadrilateral are parallel or perpendicular.Parallel lines are lines that do not meet at any point in the x y xy x y-plane. Theorem 106: If the slopes of two lines are opposite reciprocals of one another, or the product of their slopes is −1, then the lines are nonvertical perpendicular lines. Find the equation of the line perpendicular to GH which passes through the point (-4,0). Find the equation of the line which is parallel to the given line and passes through (-3,7). A line passes through the points (1,3) and (6,2). Theorem 105: If two nonvertical lines are perpendicular, then their slopes are opposite reciprocals of one another, or the product of their slopes is −1. through (-4,-4) which is perpendicular to this line. Also, the absolute values of their slopes are reciprocals. Other contents: parallel and perpendicular lines. If two lines are perpendicular and neither one is vertical, then one of the lines has a positive slope, and the other has a negative slope. A worksheet to help practice identifying whether a line is parallel or perpendicular to another line based on the slope. The opposite reciprocal of 8 is, so the lines are perpendicular. The given lines are written in y mx + b form, with m 8 for the first line and m for the second line. Theorem 104: If two lines have the same slope, then the lines are nonvertical parallel lines. Determine whether the lines y 8x + 5 and are parallel, perpendicular, or neither. Theorem 103: If two nonvertical lines are parallel, then they have the same slope. If they are nonvertical, their steepness is exactly the same.
If lines are parallel, they slant in exactly the same direction.
Determine the equation of the line that is parallel to the given line, through the given point.
The calculator will generate a step-by-step explanation on how to obtain the result. This calculator find and plot equations of parallel and perpendicular to the given line and passes through given point. Then, graph each pair on the same set of axes. Parallel and perpendicular line calculator. Determine if each pair of lines are parallel, perpendicular, or neither.