Difference between Distance and Midpoint Calculator

Additionally, in Mathematics, the midpoint is defined as the centre point of a line segment. It’s equidistant from both endpoints of the line segment and splits the line segment into two halves. Within a line segment, the midpoint represents the singular point that perfectly bisects the segment into two halves.

One can quickly determine the distance and midpoint of given coordinates using the Distance and Midpoint Calculator, which employs the distance and midpoint formulas. The key difference between Distance and Midpoint Calculators lies in their respective functions for calculating distances and midpoints on a coordinate plane. Simply input the coordinate values; the distance and midpoint calculator geometry will quickly provide the distance and midpoint values.

The Distance and Midpoint Formulas

Distance between two points

Assuming that the coordinates of the endpoints of the hypotenuse are \((x_1, y_1)\) and \((x_2, y_2)\), the calculation formula for the distance between these two points is analogous to the rule of a right triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Distance Formula

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint Formula

The midpoint is the point on a line equidistant from two points, \(A (x_1, y_1)\) and \(B (x_2, y_2)\).

The midpoint can be found by taking the average of each segment coordinate, which creates a new coordinate point. If the coordinates of the endpoints of the segment are \((X_1, Y_1)\) and \((X_2, Y_2)\), then the midpoint can be obtained by adding the values in the parentheses and dividing each result by 2.

Where \(X_1\) and \(X_2\) denote the values of the X-coordinate on the X-axis, while \(Y_1\) and \(Y_2\) represent the values of the Y-coordinate on the Y-axis.

Finding the Distance and Midpoint between two Points

Below is an example demonstrating the application of the distance formula to calculate the distance between two points on the coordinate plane. However, if you want to avoid manual calculation, the midpoint calculator geometry online is a powerful tool that can quickly calculate the midpoint of a line segment, saving you time and effort.

Our objective is to compute the distance between the two points \((4, 3.5)\) and \((-3, 1)\). It is observable that the line connecting these two points represents the hypotenuse of a right triangle. The legs of this triangle are parallel to the axes, allowing for effortless measurement of their length.

The Pythagorean Theorem will be employed to determine the length of distance d.

\(d^2 = 2.5^2+ 7^2\)

\(d^2= 6.25 + 49\)

\(d^2= 55.25\)

\(\sqrt{d^2}=\sqrt {55.25}\)

\(d= 7.43\)

The distance formula provides a technique for calculating the distance between two points in a coordinate plane.

Finding Midpoint

So given the points \((4, 3.5)\) and \((-3, 1)\), you would solve for the midpoint like this:

\(x_1 = 4\)
\(x_2 = -3\)
\(y_1 = 3.5\)
\(y_2 = 1\)

Solution

\((x_m,y_m) =(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\)

\((x_m,y_m) =(\dfrac{4 +(-3)}{2},\dfrac{3.5 + 1}{2})\)

\((x_m,y_m) =(\dfrac{1}{2},\dfrac{4.5}{2})\)

\((x_m,y_m) =(0.5,2.25)\)

Alternatively, for quick calculations you can find Midpoint Calculator here by The Mathematics Master.