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Coordinate Geometry

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

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 912
Access to these problems requires a Membership.

Arc to Area
 Annie Fetter

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.
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Calculating String Length
 Annie Fetter

Geometry, difficulty level 2. Given the archery targets of two competitors, figure out which one has the shortest 'string length'.
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The Coordinated Quadrilateral
 Annie Fetter

Geometry, difficulty level 3. A quadrilateral has vertices at (3,6), (1,2), (7,4), and (5,4). What kind of quadrilateral is it?
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Coordinated Triangle?
 Annie Fetter

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

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 square units, where can the third vertex be? What if the triangle is also isosceles?
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A Line of Reflection
 Annie Fetter

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

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

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

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'seye.
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Taxicab Distances
 Annie Fetter

Geometry, difficulty level 1. Find a general formula for distance in a taxicab geometry universe.
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The North Hunterdon Triangle
 Annie Fetter

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

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

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

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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Where's J?
 Annie Fetter

Geometry, difficulty level 2. Given an isosceles triangle with one base vertex (O) on the origin, the other base vertex (J) on the positive xaxis, and the top vertex at the point (e,f), find the coordinates of J.
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Where's Juanita Walking?
 Lillian Ray and Annie Fetter

Geometry, difficulty level 4. Help Juanita figure out how many possible ways she could walk to work.
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Who Wants to be an Archery Champion?
 Annie Fetter

Geometry, difficulty level 2. To determine the winner, calculate the "string length" for each of two archery rounds.
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