Parallel Lines        Congruent Tri.        Congruent R. Tri.        Isosc. and Equil.        Quadrilaterals        Parallelograms        Ratios        Similar Polygons        Special Triangles       Circles        Area    Coordinate Geo.        Triangle Ineq.        Solids        Computer Fun

On this page, we hope to clear up any problems that you might have with coordinate geometry.  Scroll down or click any of the links below to start understanding coordinate geometry better! Midpoint formula Slope of lines Equations of lines Distance formula Quiz on Coordinate Geometry A midpoint is a point that denotes the middle of any given line segment.  The Midpoint Theorem says the x coordinate of the midpoint is the average of the x coordinates of the endpoints and the y coordinate is the average of the y coordinates of the endpoints. If a line segment has the end points (x1, y2) and (x2, y2), the midpoint is given by the following formula: [((x1 + x2)/2), ((y1 + y2)/2)]. 1. Problem: Find the coordinates (x,y) of the midpoint of the segment that connects the points (-4, 6) and (3, -8). Solution: x1 + x2 -4 + 3 -1 1 x = ------- = ------ = -- = - - 2 2 2 2 y1 + y2 6 + (-8) -2 y = ------- = -------- = -- = -1 2 2 2 The answer: (-.5, -1) Back to Top  Finding the slope of a line is a topic usually covered in Algebra I (Elementary Algebra) courses.  We followed this custom on our site.  You can click here to go to a page that describes the process of finding the equation of a line (finding the slope is a main step in this process). Back to Top  Finding the equation of a given line is usually covered in Algebra I (Elementary Algebra) courses.  This custom was followed on this site.  You can click here to go learn about finding the equation of a line. Although finding the equation of a line is covered, you sometimes get more complex problems where you are given some information about a graph and are expected to find the equation of the line described. 1. Problem: Write the equation of the line that passes through the point (2, -3) and has a slope of (1/2). Use slope-intercept form. Solution: Write the general equation used for the slope-intercept form. y = mx + b Plug in any given information. -3 = (1/2)2 + b -3 = 1 + b -4 = b Write the equation of the line in slope-intercept form: y = .5x - 4 Back to Top  The distance formula says that the distance d between any two points with coordinates (x1, y1) and (x2, y2) is given by the following equation: d = SQRT[(x2 - x1)2 + (y2 - y1)2]. 1. Problem: Find the distance between (-2, 3) and (8, -1). Solution: Plug any given information into the distance equation. d = SQRT[(8 - (-2))2 + (-1 - 3)2] Simplify. d = SQRT[102 + (-4)2] d = SQRT(100 + 16) d = 2(SQRT(29)) Back to Top  Take the Quiz on coordinate geometry.  (Very useful to review or to see if you've really got this topic down.)  Do it!