Math Forum - Problems Library - Coordinate Geometry

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Geometry
  lines/angles
  triangles
  quadrilaterals
  polygons
  circles
  perimeter, area,
    volume
  similar/congruent
  right triangles
  transform/symmetry
  construction/locus
  coordinate geometry
  modeling/applications

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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 9-12


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. ... more>>

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'. ... more>>

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? ... more>>

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? ... more>>

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? ... more>>

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'. ... more>>

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. ... more>>

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. ... more>>

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's-eye. ... more>>

Taxicab Distances - Annie Fetter
Geometry, difficulty level 1. Find a general formula for distance in a taxicab geometry universe. ... more>>

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. ... more>>

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. ... more>>

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''. ... more>>

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. ... more>>

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 x-axis, and the top vertex at the point (e,f), find the coordinates of J. ... more>>

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. ... more>>

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. ... more>>

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