Distance between two points and the midpoint

The distance formula is an algebraic expression used to determine the distance between two points with the coordinates \( (x_1, y_1)\) and \( (x_2, y_2)\).

$$D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$$

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Example

Find the distance between (-1, 1) and (3, 4).

This problem is solved simply by plugging our x- and y-values into the distance formula:

$$D=\sqrt{(3-(-1))^{2}+(4-1)^{2}}=$$

$$=\sqrt{16+9}=\sqrt{25}=5$$

Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.

If the end points of a line segment is (x₁, y₁) and (x₂, y₂) then the midpoint of the line segment has the coordinates:

$$\left(\frac{x_{1}+x_{2}}{2},\: \frac{y_{1}+y_{2}}{2}\right)$$

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Video lesson

Find the midpoints between the coordinates (-4, -1) and (6,7)