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Browse High School Coordinate Plane Geometry

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



Express y-Coordinate of Point... [8/9/1996]
P and Q are the points of intersection of the line y/2+x/3 = 1 with the x- and y- axes respectively. The gradient of QR is 1/2 and R is the point whose x-coordinate is 2t, where t is positive....

Find Circle Center and Radius [09/21/2001]
Given three sets of (x,y) coordinates that lie on the circumference of a circle, how do you find the center and radius of the circle?

Finding a Point Equidistant From Two Other Points [8/18/1996]
Point A is (-5,-3), and point B is (-1,-5); to be equidistant from A and B, what should the value of k be for the point (3,k)?

Finding a Point on a Circle [5/28/1996]
How do I find the y1 value?

Finding Coordinates [12/31/1996]
Given two intersecting line segments, the angle they form at their intersection, the coordinates of one endpoint and those of the intersection, and the length of one of the line segments, how do you determine the coordinates of the remaining endpoint?

Finding Equations of Angle Bisectors between Two Lines [08/14/2004]
Is there any way or formula to find the coordinates of points which lie on the line that bisects the angle between two given lines?

Finding Points on a Line in Slope-Intercept Form [07/29/2005]
I have a line y = kx + b, and I know point A(x1, x2) is on the line. If point B is also on the line, and the distance between A and B is d, what are the possible point(s) B?

Finding the Area of Overlap between Two Circles [04/16/2008]
Suppose I know the centers and radii of two circles that overlap. How can I find the area of that overlapping region?

Finding the Center of a Circle from 2 Points and Radius [01/24/1997]
Given two points on a circle and the circle's radius, find the center coordinates of the circle.

Finding the Center of a Circle from 2 Points [06/01/1999]
How do you find the centre of a circle if you are given 2 points on the circle and the radius?

Finding the Center of a Circle from Three Points [05/22/2000]
How can I find the coordinates of the center of a circle, given the coordinates of three points on its circumference?

Finding the Center of a Circle Given 3 Points [05/25/2000]
How can I find the coordinates of the center of a circle given the x and y coordinates of 3 points that lie on its circumference?

Finding the Coordinates of a Triangle Vertex [10/26/1999]
How can I find the coordinates of the point A of triangle ABC if B lies on the line 3y = 4x, C lies on the line y = 0, the line BC passes through (2/3,2/3) and AOBC forms a rhombus (where O is the origin)?

Finding the Equation of a Reflected Graph [04/24/2004]
When you reflect the graph of an equation over an axis or a given line, is there a way to determine what the equation of the reflection will be without having to graph it first?

Finding the Other End of a Line Segment [07/25/2002]
Given a point, the slope of a line segment, and a length, how do I find the other end of the line segment?

Finding Triangle Vertices from Midpoints [09/18/1999]
If you know the coordinates of the midpoints of the sides of a triangle, how can you find the coordinates of its vertices?

Find the Coordinates of Point p [10/22/2002]
Point P lies on the line y=x. The coordinates of Q and T are (-1,8) and (8,1) respectively. The sum of the distances QP and TP is 18 units. Determine the coordinates of P.

Find the Length of a Carpet [5/3/1996]
A carpet is placed diagonally in a rectangular room...

Find the Orthocenter [11/04/1998]
Given three points (-2,4) (7,2) (3,8), find the orthocenter.

Foci of an Ellipse [06/08/2001]
If the major and minor axis of an ellipse are given, how do I find the focus points?

Formula for Laying Out an Arc [09/27/2002]
I need a formula for laying out an arc using a known radius and distance from the chord to the arc at 90 degrees.

Geometric Proof of a Limit [12/06/2003]
Prove that lim[x->0](sinx)/x = 1 without using L'Hopital's rule.

Given a Triangle with Angles a,b,c [05/03/1999]
Show that cos(a)+cos(b)+cos(c) is less than or equal to 3/2.

Graphing an Ellipse [11/20/1998]
How do you graph an ellipse? What is the equation?

Heron's Formula, Cartesian Coordinate Plane [11/01/2001]
If a triangle has sides 5, 6, and the square root of thirteen, what is the area of the triangle?

History of Abscissa [03/26/2001]
Where does the word abscissa come from?

How Do You Do Translations? [12/09/2009]
If (4,7) translates to (-3,9) what is the translated x-coordinate for the point (10,-5)?

The Incenter and Euler's Line [11/27/2001]
Why is the incenter of a triangle not on the Euler line?

Inscribed Angle, Circle Equation [6/14/1996]
What's an inscribed angle? What's the equation for a circle with a center at (8,-1) and a radius of 15?

Intersection Points [03/13/1999]
A line goes through the point A(1, 2) to cut 2y = 3x-5 at P and x+y = 12 at Q. If AQ = 2AP, find the coordinates of P and Q.

Introduction to Quadrants in the Coordinate Plane [02/05/2004]
What is a quadrant? How do you find it? I had to identify 9 ordered pairs on a graph. Now I need to also name the quadrant each one is in.

Is This a Square? [01/30/2001]
Given four points on a graph, what can I do to verify this is a square?

Lattice Points and Boundary Lattice Points [08/30/1998]
What is an interior lattice point and a boundary lattice point of a given shape (triangle, circle, rectangle, etc.)?

Lattice Points and Equilateral Triangles [12/08/2002]
Can an equilateral triangle have lattice points as its vertices?

Lattice Points in a Rectangle [06/04/1999]
How can I prove that in any rectangle centered at (0,0) with an area greater than 4, you can find lattice points other than (0,0)?

Lattice Points on Hypotenuse [10/01/2001]
What is the number of lattice points on the hypotenuse of a right triangle?

Length of the Diagonals of a Parallelogram [05/22/2000]
A parallelogram has a 70-degree angle and sides 6cm and 10cm long. How long are its diagonals?

Light Beam Reflection [01/31/2002]
Four mirrors form a rectangle 3 m by 2 m. A light beam is shone from A at 45 degrees. Which corner does the beam strike first?

Line and Unit Circle; Pythagorean Triples [04/16/2001]
If (X,Y) is a point in the 1st quadrant on the unit circle and m is the slope of the line passing through (X,Y) and the point (0,-1), how can I express the coordinates (X,Y) in terms of m? Can this be used to generate Pythagorean triples?

Line Dividing a Plane [05/11/2001]
Given a square (graphed on the Cartesian coordinate system) and a point in the square, draw a line through the point that will divide the square into two regions: one the smallest area possible, the other the largest possible.

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