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Coordinate Geometry
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The use of the coordinate plane as a backdrop for algebraically
related problems affords students practice with algebraic
manipulations of geometric concepts. Many of these problems
involve the distance formula or slope, and require students to
fix the origin appropriately and find coordinate pairs for other
pertinent information in the problem.
- Related Resources
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Interactive resources from our Math Tools project:
Geometry: Coordinate Geometry
The closest match in our Ask Dr. Math archives:
High School: Coordinate Plane
NCTM Standards:
Geometry Standard for Grades 9-12
Access to these problems requires a Membership.
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Arc to Area
- Annie Fetter
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Geometry, difficulty level 4. Given an arc with a measure of 40 degrees whose endpoints are at (1,5) and (5,3), find the area of the circle that contains the arc.
... more>>
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Calculating String Length
- Annie Fetter
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Geometry, difficulty level 2. Given the archery targets of two competitors, figure out which one has the shortest 'string length'.
... more>>
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The Coordinated Quadrilateral
- Annie Fetter
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Geometry, difficulty level 3. A quadrilateral has vertices at (-3,6), (-1,-2), (7,-4), and (5,4). What kind of quadrilateral is it?
... more>>
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Coordinated Triangle?
- Annie Fetter
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Geometry, difficulty level 3. Triangle ABC has an area of 24 units^2. Point A is at (6,0); point B is at (10,0). Where can point C be? What if the triangle is
isosceles?
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Descartes' Triangle?
- Annie Fetter
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Geometry, difficulty level 3. Two vertices of a triangle are located at (0,6) and (0,12). If the area of the triangle is 12 units^2, where can the third vertex be? What if the triangle is also isosceles?
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Finding Formulas for Medians from Edgelengths
- Annie Fetter
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Geometry, difficulty level 3. Write a formula for finding the median of a triangle in terms of the three sides of the triangle.
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A Line of Reflection
- Annie Fetter
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Geometry, difficulty level 2. Find the equation of the line of reflection for triangle ABC and its
image, A'B'C'.
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Mirror, Mirror
- Annie Fetter
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Geometry, difficulty level 2. In the given image, the green polygon is a reflection of the purple
polygon. Find the equation of the line of reflection.
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Rotating a Triangle
- Annie Fetter
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Geometry, difficulty level 2. Given a triangle on a coordinate grid, find the new coordinates of the vertices if you rotate the triangle 90 degrees about the origin.
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Sighting in a Rifle
- Annie Fetter
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Geometry, difficulty level 3. Analyze the given target of four shots, and tell me how far to move the scope on my rifle so that the group of shots will be centered around the bull's-eye.
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The North Hunterdon Triangle
- Annie Fetter
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Geometry, difficulty level 2. Given points O:(0,0) and Q:(a,0), describe the possible locations of
point P such that triangle OPQ is first isosceles and then equilateral.
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Transforming a Triangle
- Annie Fetter
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Geometry, difficulty level 1. Given two triangles on a coordinate plane, find a pair of transformations that will map the first triangle onto the second triangle.
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Triangle in Motion?
- Annie Fetter
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Geometry, difficulty level 2. Given triangle ABC, the triangle is translated and then reflected, and
the locations of A' and A'' are given. Find the locations of B'' and C''.
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Triangle Transformation
- Annie Fetter
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Geometry, difficulty level 3. Given triangles ABC and DEF on the coordinate plane and a list of transformations, explain how to map ABC onto DEF in only two steps.
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Two Houses and a Carrier Pigeon
- Annie Fetter
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Geometry, difficulty level 3. One house is 300 yards from a highway. 1200 yards down the highway is the driveway to another house, 600 yards from the highway, on the same side of the road. What is the shortest distance between the two houses if you go to the highway in between?
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Who Wants to be an Archery Champion?
- Annie Fetter
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Geometry, difficulty level 2. To determine the winner, calculate the "string length" for each of two archery rounds.
... more>>
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