Willow Tree
Midpoint and Distance Formulas
The shortest distance between two points is a straight line. Learners use the Pythagorean Theorem to develop a formula to find that distance. They then find the midpoint using an average formula.Â
Del Mar College
All About Lines
This resource should be called "All About Lines, and Then Some!". Packed full of all the key components of linear functions, learners review how to set up different equations, find intercepts, and graph. All the main topics are included...
Curated OER
The Distance and Midpoint Formula
In this college level mathematics worksheet, students solve use the Pythagorean Theorem to find the missing side of a right triangle and explore the connection between the Pythagorean Theorem and the distance formula. Â Â Students also...
Corbett Maths
Shortest Distance between Line and Point
A short video shows how to find the shortest distance between a line and a point on the coordinate plane. Using the fact the shortest distance is the perpendicular, the presenter shows the class how to find the intersection of the two...
EngageNY
The Distance from a Point to a Line
What is the fastest way to get from point A to line l? A straight perpendicular line! Learners use what they have learned in the previous lessons in this series and develop a formula for finding the shortest distance from a point to a...
Virginia Department of Education
Distance and Midpoint Formulas
Small groups work through two guided activities to derive the distance and midpoint formulas for the coordinate plane. The activities begin with concrete examples and move to abstract.
EngageNY
Every Line is a Graph of a Linear Equation
Challenge the class to determine the equation of a line. The 21st part in a 33-part series begins with a proof that every line is a graph of a linear equation. Pupils use that information to find the slope-intercept form of the equation...
EngageNY
The Slope of a Non-Vertical Line
This activity introduces the idea of slope and defines it as a numerical measurement of the steepness of a line. Pupils then use the definition to compare lines, find positive and negative slopes, and notice their definition holds for...
Mt. San Antonio Collage
Isosceles Triangles and Special Line Segments
Under which conditions can a triangle be classified as isosceles? High schoolers practice identifying isosceles triangles and special line segments, including angle bisectors, medians of triangles, and perpendicular bisectors of sides of...
EngageNY
The Line Joining Two Distinct Points of the Graph y=mx+b Has Slope m
Investigate the relationship between the slope-intercept form and the slope of the graph. The lesson plan leads an investigation of the slope-intercept equation of a line and its slope. Pupils realize the slope is the same as the...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
EngageNY
More on Modeling Relationships with a Line
How do you create a residual plot? Work as a class and in small groups through the activity in order to learn how to build a residual plot. The activity builds upon previous learning on calculating residuals and serves as a precursor to...
CK-12 Foundation
Midpoint and Segment Bisectors: The Midpoint Formula
Let's meet in the middle. Given two points on the coordinate plane, pupils use the interactive to find the midpoint. The interactive provides a graphical display of the midpoint and the midpoint formula with the coordinates of the...
CK-12 Foundation
Vectors as Directed Line Segments: Directed Line Segment
Direct your class' attention to directed line segments. The interactive resource allows pupils to create segments with specific endpoints. Scholars plot the initial and terminal points to determine the direction and magnitude of the...
Curated OER
Finding the Slope of a Line Through Two Given Points
In this slope of a line worksheet, students use the slope formula to determine the slope of a line passing through a given point. This one-page worksheet contains ten problems, with answers.
Curated OER
Length of a Line Segment - Distance
Pupils determine the distance between two given points. They use the distance formula to determine line length, as well as the length of the radius of a circle. The Pythagorean Theorem may also be used to determine line length. This...
Education Development Center
Points, Slopes, and Lines
Before graphing and finding distances, learners investigate the coordinate plane and look at patterns related to plotted points. Points are plotted and the goal is to look at the horizontal and vertical distances between coordinates and...
Curated OER
Point-Slope Form of a Line
This activity helps young mathematicians connect the graph and the point-slope form of a line, by first solving a real-world problem and then using that example to motivate the understanding of the equation. By manipulating the gizmo,...
Curated OER
WS 10.4 Organic Naming
In this organic molecules worksheet, students are given fifteen organic molecules to name, write the structural formula, write the line formula, write the condensed structural formula and write the molecular formula.
Curated OER
WS 10.7 Organic Nomenclature, Part 2
In this organic molecules activity, students are given fifteen organic molecules to name, write the complete structural formula, write the line formula and write the condensed structural formula.
Curated OER
WS 10.10- More Organic Reactions
For this organic reactions worksheet, students write structural formulas for five alkenes. They also write equations and structural or line formulas for five reactions.
EngageNY
The Computation of the Slope of a Non-Vertical Line
Determine the slope when the unit rate is difficult to see. The 17th part of a 33-part series presents a situation that calls for a method to calculate the slope for any two points. It provides examples when the slope is hard to...
EngageNY
Equations for Lines Using Normal Segments
Describing a line using an algebraic equation is an essential skill in mathematics. The previous lesson in the series challenged learners to determine if segments are perpendicular with a formula. Now they use the formula to determine...
Concord Consortium
Line of Sight
There's no way around it—learners must use trigonometry to model the line of sight around a race track! Using the starting line as the origin, pupils model the straight line distance to any car using a trigonometric expression. The...