Slope & Distance Calculator

About the Slope & Distance Calculator

Given two points in the plane, this finds the slope of the line through them, the straight-line distance, and the midpoint.

How to use this calculator

1. Enter the first point as 2x_1, y_12x and the second point as 2x_2, y_22x.
2. Click calculate to find the slope, distance, and midpoint.
3. Check the slope to see whether the line rises, falls, is flat, or is vertical.
4. Use the step-by-step result to understand how each value was found.

The formula explained

The slope formula computes the rate of change between two points, and the distance formula computes the straight-line distance between them. The midpoint is found by averaging the x-coordinates and the y-coordinates.

• \(x_1\) = the x-coordinate of the first point
• \(y_1\) = the y-coordinate of the first point
• \(x_2\) = the x-coordinate of the second point
• \(y_2\) = the y-coordinate of the second point
• m = the slope of the line through the two points
• d = the distance between the two points

Step by step method

1. Find the change in y by subtracting y_1 from y_2, and the change in x by subtracting x_1 from x_2.
2. Compute the slope with m = (y_2 - y_1)/(x_2 - x_1), and compute the distance with d = 2sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}2.
3. Find the midpoint by averaging the x-values and averaging the y-values: ((x_1 + x_2)/2, (y_1 + y_2)/2).

Worked example

Problem. Find the slope, distance, and midpoint between the points (2, 3) and (8, 11).

1. Slope: m = (11 - 3)/(8 - 2) = 8/6 = 4/3.
2. Distance: d = 2sqrt{(8 - 2)^2 + (11 - 3)^2}2 = 2sqrt{6^2 + 8^2}2 = 2sqrt{36 + 64}2 = 2sqrt{100}2 = 10.
3. Midpoint: ((2 + 8)/2, (3 + 11)/2) = (5, 7).

Tips and common mistakes

• If x_2 = x_1, the line is vertical, so the slope is undefined because you would be dividing by 0.
• Be careful with subtraction signs, especially when one coordinate is negative.

Frequently asked questions