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Browse High School Coordinate Plane Geometry

Stars indicate particularly interesting answers or good places to begin browsing.

10 Square Units on Dot Paper [03/01/2003]
How can I draw a square with 10 square units on dot paper?

2D Coordinate System [05/13/1999]
I have two 2D coordinate systems S1 and S2 arbitrarily positioned on a plane... determine the relative positions of S2 and S1.

3d Distance [11/1/1994]
What's the easiest way to find the distance between a point and a line in three dimensions: When the line is defined by two points in space, and when the line is defined by angles from the cartesian axes?

Absolute Degrees in Terms of One Circle Revolution [05/02/2002]
I have an angle of -6 degrees which I need to express in terms of a single 0-360 revolution.

Angle Between Two Sides of a Pyramid [10/29/1999]
How can I compute the angle formed by two sides of a frustrum of a pyramid?

Area of a Polygon [06/27/1997]
If you know the coordinates of the vertices, how do you calculate the area of a polygon?

Area of Bermuda Triangle [06/10/2001]
The Bermuda triangle is shown on a graph with the points A(1,2) B(4,8) and C(8,1). Determine the area of the triangle two different ways.

Area of Intersection of Two Circles [12/1/1995]
My teenage son asked me for the formula for the area of intersection of two arbitrary circles.

Area of Polygon [08/20/1999]
Using coordinate system to find the areas of polygons.

Ball Thrown between Trains [10/15/2003]
Two trains A and B each of length 100m travel in opposite directions in parallel tracks. The speeds are 20m/s and 30m/s respectively. A boy sitting in the front end of train A throws a ball to a boy sitting in the front end of train B when they are at the closest distance. The speed of the ball is 2m/s. The ball, instead of reaching the boy, hits the rear end of the train. Find the distance between the parallel tracks.

Barycentric Calculus [01/06/1999]
How does barycentric calculus compare with trilinear or cartesian calculus?

Bouncing Cue Ball [10/29/1996]
A cue ball is launched at an angle of 45 degrees from the lower left corner of a pool table and ends up in the lower right corner. What rule will predict which corner the ball will hit? What patterns are involved?

Calculating the Angle of a Plank [08/22/2001]
Are there any equations that could be used to solve for a plank of known width?

Card Stacking Problem, Redux [01/31/2017]
A teen seeks clarity on the induction steps that underpin the gravity-defying conundrum of objects balanced over an edge. By switching from torques to centers of mass, Doctor Rick works up an explicit treatment of the recursion often left as an exercise to the reader.

Center of a Circle from Circumference Points [06/25/1999]
How do I figure the center point (Xc,Yc,Zc) of a circle given 2 or more points on its circumference and its radius?

Circle Center's Cartesian Coordinates [03/24/1999]
How do you find the Cartesian coordinates of a circle's centers if you know two points on its perimeter?

Constructing Tangents to Circles [05/08/2002]
How do you construct a line tangent to a circle through a point outside the circle? How do you do it with only a straightedge?

Coordinate Geometry [08/21/1998]
Given two coordinate points in the Cartesian plane, locate a third point perpendicular to the line joining points 1 and 2 and a certain distance from either point.

A Coordinate Geometry Problem [11/26/1996]
Given two perpendicular lines AC and BD in a plane and a point E directly above their intersection, find the length of BC.

Coordinate Pairs with Zeros [03/15/2004]
If a coordinate pair contains a zero, which quadrant is it in? For example, is the point (2,0) in the 1st or 4th quadrant?

Coordinates of a Point [6/12/1996]
ABC is a right-angled triangle labeled counter-clockwise with its point C lying on the line y=3x. A is (2,1) and B is (5,5). Find the two possible coordinates of C.

Coordinates of Right Triangles [06/25/1997]
Find all possible values of k so that (-1,2), (-10,5), and (-4,k) are the vertices of a right triangle.

Coordinates of Two Points [04/23/2002]
My teacher asked for the coordinates of two points that lie on the x- axis. I wrote (0,4) and (0,98)...

Coordinate Systems [04/22/1997]
What is the polar coordinate system and how does it differ from the rectangular coordinate system?

Coordinate Systems, Longitude, Latitude [04/19/1997]
Can you explain pitch, roll, and yaw to me? Are there other systems for measuring an object's position in space?

Coordinate Transformations [06/25/2003]
What equation can be used to determine the new point when you rotate a point some number of degrees around another point?

Degrees of Freedom [12/17/2002]
What is meant by 'degrees of freedom'?

Deriving the Distance Formula from the Pythagorean Theorem [03/23/2003]
How does one derive the distance formula from the Pythagorean theorem?

Deriving the Dot Product [09/17/1998]
Can you explain how to derive the formula for the dot product?

Deriving Trilinear Coordinates [05/18/1999]
How do you derive the trilinear coordinates of the orthocenter of a triangle?

Determinants and the Area of a Triangle [12/14/1998]
Given a triangle with vertices (A,B), (C,D), and (E,F), how do you find the area in determinant form?

Determining the Equation of a Circle [05/12/2000]
How can I determine which of five equations describes the set of all points (x,y) in the coordinate plane that are a distance of 5 from the point (-3,4)?

Diameter of a Circle Circumscribed Around a Triangle [05/13/1998]
Applying the Pythagorean Theorem to find the diameter of the circle circumscribed around a triangle with side lengths 25, 39, and 40.

Distance between Point and Line [02/08/2009]
How far from the line 3x + 6y = 10 is the point (1,2)?

Dividing a Line Segment into Equal Parts [11/22/2004]
I have two endpoints of a line segment with coordinates A(2, 7) and B(-4, -2). I am looking for the coordinates of the points that divide AB into 3 equal parts.

Ellipse Equation [03/11/1999]
How do I get the equation of an ellipse, given four points and the inclination of the major axis?

Ellipse Geometry [08/09/1998]
I wish to draw a line departing at a given angle from the long axis of an ellipse and bisecting the perimeter of the ellipse at right angles to the tangent at that point...

Endpoint of an Arc [06/25/2001]
Given the center of the circle, the angle of the arc, the radius of the circle, and the starting point of the arc, determine the end point of the arc using cartesian coordinates.

Equal Area and Perimeter: Rectangles [09/09/2001]
There are only two rectangles whose area is exactly the same as their perimeter if the dimensions of each are whole numbers. What are the dimensions?

Equation of a Rectangle? [11/11/2012]
A student wonders if there is an equation for a rectangle in the Cartesian plane, comparable to the one for the equation of a circle. Doctor Peterson confirms the student's suspicions about the difficulties involved.

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