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.
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Dividing Segments Proportionately
Fractions, ratios, and proportions: what do they have to do with segments? Scholars discover the midpoint formula through coordinate geometry. Next, they expand on the formula to apply it to dividing the segment into different...
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Coordinate Geometry Battleship Lesson Plan
Students play a "Battleship" type of game to practice graphing on a coordinate plane. In this coordinate graphing lesson, students select a point on their grid to place their "battleship." It the opposing team misses the ship, the...
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Distance and Complex Numbers 2
Classmates apply midpoint concepts by leapfrogging around the complex plane. The 12th instructional activity in a 32 segment unit, asks pupils to apply distances and midpoints in relationship to two complex numbers. The class develops a...
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Midpoint Formula in the Coordinate System
Students calculate the midpoint of a line. In this geometry lesson, students identify the different parts of the coordinate plane. They use the midpoint formula to find the middle of segments between a pair of coordinates.
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Quadrilateral Explorations-Grade Nine
Ninth graders investigate quadrilaterals. In this geometry lesson, 9th graders examine and classify quadrilaterals using the slope, midpoint and distance formulas. Additionally, students create various quadrilaterals given...
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Finding the Distance and Midpoint of a Line Segment
Students use the Pythagorean formula to find the length of a line. Afterward, they explore the midpoint formula to determine the midpoint of a line with a non-zero slope on a coordinate plane. Students complete assigned problems and...
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Distance and Complex Numbers 1
To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...
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Analytic Proofs of Theorems Previously Proved by Synthetic Means
Prove theorems through an analysis. Learners find the midpoint of each side of a triangle, draw the medians, and find the centroid. They then examine the location of the centroid on each median discovering there is a 1:2 relationship....
Curated OER
Distance Formula
Students calculate the distance formula. In this geometry lesson, students find the distance between two points on a coordinate plane. They identify the four different quadrants.
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Trapezoid and Midpoint Rule
Students solve problems of area using the trapezoid and midpoint rule. In this calculus lesson, students take the derivative of the functions as they approximate the area under a curve. They calculate the exact area using the area formula.
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Finding the Measure of Segments
Students observe and solve examples of betweenness, ruler postulate, and segment addition postulate. They complete the Finding the Measure of Segments worksheet using the distance formula.
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Measurement via Triangulation
Students utilize triangulation techniques to determine altitudes of objects. An altitude locator is constructed and used to determine the height of a building or a tree. Tangent tables and formulas provide the ratio for the formula to...
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Application of Properties of Quadrilaterals in the Coordinate Plane
Students apply definitions and theorems to verify special quadrilaterals
using coordinate geometry. They apply the slope formula, the midpoint
formula, and the distance formula to justify that a given quadrilateral is a
parallelogram....
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Applications of Properties of Quadrilaterals in the Coordinate Plane
Students explore the concept of quadrilaterals. In this quadrilaterals lesson, students use the slope formula, midpoint formula, and distance formula to justify that a given quadrilateral is a parallelogram.
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Coordinate Proofs
Learners explore the concept of coordinate proofs. In this coordinate proofs lesson, students write coordinate proofs using properties of distance, slope, and midpoint. Learners discuss why it is sometimes beneficial to double the...
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Conic Sections
Students explore the different properties of conics. In this algebra lesson, students calculate the midpoint of a line, the distances between two points as they get ready to find the focus and directrix in eclipse and other conics. They...
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Equations of Lines
Students classify lines, slopes and shapes. In this calculus lesson, students calculate the midpoint, segment and equation of a circle. They also review what a slope and angle of inclination is.
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CSI Investigation
Students solve real life situation using the Pythagorean Theorem. In this geometry lesson, students calculate the length, midpoint and slope of segments. They solve word problems using properties of square roots.
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Isosceles Triangles
Students identify the properties of an isosceles triangle. In this geometry lesson, students find the midpoint, median and angle bisector of a triangle. They construct angle bisectors and measure missing angles.
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This Building is Tall
Students calculate the perimeter of shapes. In this geometry lesson, students relate properties of polygons to the real world. They find length, midpoint and slope.
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Hexagon Island
Students identify different polygons. In this geometry lesson, students name polygons using the number of sides. They calculate distance and slopes using the correct formula.
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Exploring Centers of Triangles
Students explore properties of triangles using angle bisectors, incenters, circles, midpoints, and altitudes. They use Geometer's Sketchpad in order to create triangles and their properties.
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Quadrilateral Explorations
Ninth graders identify quadrilaterals and label the vertices of quadrilaterals. they justify their identification of the quadrilaterals. Students work in groups to identify and create quadrilaterals