Equations of Perpendicular and Parallel Lines and Applications
Lessons in this chapter
About Equations of Perpendicular and Parallel Lines and Applications
Equations of Perpendicular and Parallel Lines and Applications applies algebra to the coordinate plane, connecting Algebra 1's linear equations work to geometric figures.
Midpoint and Distance Formulas covers finding the exact middle point between two coordinates and calculating the exact distance between them, both built from the Pythagorean Theorem.
Parallel and Perpendicular Lines uses slope to identify or write the equation of a line parallel (same slope) or perpendicular (negative reciprocal slope) to a given line.
Area and Perimeter closes the chapter by applying the distance formula to find the side lengths of a figure plotted on the coordinate plane, then calculating its area and perimeter from those real coordinate-based measurements.
This chapter is three lessons long and each opens as a Geometry worksheet in the page: Midpoint and Distance Formulas, Parallel and Perpendicular Lines, and Area and Perimeter. Every question is marked as you answer it, so a perpendicular slope taken as the negative rather than the negative reciprocal is caught at once. Free to try, with no login needed for your first 3.
Frequently asked questions
Midpoint and Distance Formulas puts geometric figures on the coordinate plane, finding the point halfway between two others and the distance between them straight from their coordinates. Parallel and Perpendicular Lines writes the equation of a line through a given point that is parallel or perpendicular to another, using equal slopes in one case and negative reciprocal slopes in the other. Area and Perimeter then applies those tools to figures drawn on the plane. The chapter sits in the high school Geometry conceptual category (G).
The midpoint formula finds the exact middle point between two coordinates by averaging their x-values and averaging their y-values separately.
The distance formula, d = √((x₂-x₁)² + (y₂-y₁)²), comes directly from the Pythagorean Theorem: the horizontal and vertical differences between two points form the legs of a right triangle, and the distance between them is the hypotenuse.
Two lines are parallel if and only if they have the exact same slope (and different y-intercepts, otherwise they’re the same line).
Two lines are perpendicular if and only if their slopes are negative reciprocals of each other, multiplying the two slopes together always gives -1.
Use the distance formula to find each side’s exact length from its coordinate endpoints, then apply the perimeter or area formula for that specific shape using those calculated lengths.