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
Slope of lines
Equations of lines
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.
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)
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).
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.
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
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))
Take the Quiz on coordinate geometry. (Very useful to review or to see if you've really got this topic down.) Do it!