Calculate midpoints, distances, slopes, line equations, and intersections on an interactive coordinate plane.
Coordinate Geometry Toolkit turns plotted or entered Cartesian points into the standard relationships between them: midpoint, straight-line distance, slope, and the equation of the line through two points. It can also compare two lines and identify their intersection on the coordinate plane. A common surprise is that a vertical line has no finite slope and cannot be written in slope-intercept form; its equation is x = constant.
A concrete input and expected output from the current implementation.
Input
Point A = (0, 0); Point B = (3, 4)
Expected output
Midpoint: (1.5, 2); distance: 5; slope: 4/3; line equation: y = (4/3)x
The midpoint averages x and y separately: ((0 + 3)/2, (0 + 4)/2) = (1.5, 2). The coordinate differences are 3 and 4, so the distance is sqrt(3^2 + 4^2) = 5, the slope is 4/3, and the line has zero intercept because it passes through the origin.
For points A = (x1, y1) and B = (x2, y2), the midpoint averages corresponding coordinates. Distance comes from the Pythagorean relationship, and slope is the change in y divided by the change in x. The same pair determines one straight line unless the points are identical, in which case a unique line is not determined.
A nonvertical line can be shown in slope-intercept form, while a vertical line is written as x = constant. For two line equations, the intersection is the coordinate pair that satisfies both. Distinct parallel lines have no intersection, and coincident lines have infinitely many points in common rather than one unique result.
No, not for a valid pair of distinct points. Midpoint and distance are symmetric. Slope also stays the same because reversing the points reverses both coordinate differences, leaving their quotient unchanged. The line equation is unchanged as well. If the points coincide, however, neither a unique slope nor a unique line follows.
No. Distinct nonparallel lines have exactly one intersection. Distinct parallel lines never meet, so there is no intersection coordinate. Coincident lines represent the same set of points and therefore have infinitely many intersections rather than one. A vertical line can still intersect another line normally even though its slope is undefined.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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