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How This Calculator Works
Given two points on a coordinate plane, three related quantities describe how they relate: how
far apart they are (distance), the point exactly between them (midpoint), and how steep the line
connecting them is (slope). Enter both points’ x and y coordinates, and
this calculator finds all three at once.
The Formulas
Distance:(x2−x1)2+(y2−y1)2 — the Pythagorean
theorem applied to the horizontal and vertical gaps between the two points.
Midpoint:(2x1+x2,2y1+y2) —
the average of the two x-coordinates and the average of the two y-coordinates.
Slope:x2−x1y2−y1 — “rise over run.” Undefined
when both points share the same x-coordinate (a perfectly vertical line has no defined slope).
Worked Example
Point A at (1, 2) and Point B at (4, 6):
Distance: (4−1)2+(6−2)2=9+16=25=5
Midpoint: (21+4,22+6)=(2.5,4)
Slope: 4−16−2=34≈1.33
Cómo funciona esta calculadora
Dados dos puntos en un plano de coordenadas, tres cantidades relacionadas describen cómo se
relacionan entre sí: qué tan separados están (distancia), el punto exactamente entre ellos (punto
medio) y qué tan inclinada es la línea que los conecta (pendiente). Ingresa las coordenadas x e y
de ambos puntos, y esta calculadora encuentra las tres a la vez.
Las fórmulas
Distancia:(x2−x1)2+(y2−y1)2 — el teorema de
Pitágoras aplicado a las diferencias horizontal y vertical entre los dos puntos.
Punto medio:(2x1+x2,2y1+y2) —
el promedio de las dos coordenadas x y el promedio de las dos coordenadas y.
Pendiente:x2−x1y2−y1 — la variación vertical
dividida entre la variación horizontal. Indefinida cuando ambos puntos comparten la misma
coordenada x (una línea perfectamente vertical no tiene una pendiente definida).
Why are distance, midpoint, and slope combined into one calculator?
All three are computed from the exact same two points, so it's more useful to see them together than to look them up on three separate pages — you enter your coordinates once and get every commonly-needed answer at once.
What does an undefined slope mean?
A vertical line (where both points share the same x-coordinate) has no defined slope, since the slope formula would require dividing by zero. This calculator reports "Undefined (vertical line)" in that case rather than an error or a meaningless number.
What is the midpoint used for?
The midpoint is the exact center point between two coordinates — useful for finding the center of a line segment, splitting a distance evenly, or as a step in other geometry problems like finding a perpendicular bisector.
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