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- Midpoint calculator

This calculator **finds the midpoint between two points** in two or three-dimensional space.
The calculator can also determine the endpoint of a line segment given its midpoint and one endpoint.

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Solved examples:

Question 1:ex 1:

What are the coordinates of the midpoint of the line segment AB with endpoints (-4, 8) and (-2, 3)?

Question 2:ex 2:

What is the midpoint of a line segment with endpoints (-1, 4, 3/2) and (5/2, -1, 1/2)?

Question 3:ex 3:

What is the endpoint of a line segment whose midpoint is M(1,3) and second endpoint is A(4,2)?

Question 4:ex 4:

Find the second endpoint of a line segment whose middle point is M(1/2, 4, -3) and its first endpoint is A(-1/2, 4/3, 5/2).

Find more worked-out examples in the database of solved problems..

To find midpoint between points A(x1, y1) and B(x2, y2), we usually use formula:

M((x1+x2)/2 , (y1+y2)/2)

**Example:**

Find the midpoint coordinates of the line segment AB with endpoints (12, 3) and (6, 7)?

**Solution:**

In this example the constants x1, y1, x2 and y2 are x1 = 12, y1 = 3, x2 = 6, y2 = 7.

M((x1+x2)/2, (y1+y2)/2)

M((12+6)/2, (3+7)/2)

M(18/2, 10/2)

M(9, 9)

Hence, the midpoint of the segment AB is M(9, 9).

The midpoint formula in three dimensions is similar to the two-dimensional case.

M((x1+x2)/2 , (y1+y2)/2, (z1+z2)/2)

**Example:**

Find the midpoint coordinates given the endpoints are (-3, 4, 6) and (2, 1, 12)?

**Solution:**

Since the points are in space we need to find six constant: x1, y1, z1, x2, y2 and z2 x1 = -3, y1 = 4, z1 = 6, x2 = 2, y2 = 1, z2 = 12. Now we can apply midpoint formula.

M((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)

M((-3+2)/2, (4+1)/2, (6+12)/2)

M(1/2, 5/2, 9)

Hence, the midpoint is M(1/2, 5/2, 9).

The easiest way to find endpoint is by using formulas:

x2 = 2 xm - x1

y2 = 2 xm - y1

**Example:**

Find the endpoint if the middle point is M(4,7) and the second endpont is A(-2,1)

x2 = 2 xm - x1 = 2 * 4 - (-2) = 8 + 2 = 10

y2 = 2 ym - y1 = 2 * 7 - 1 = 14 - 1 = 13.

Hence, the endpoint is B(10, 13).

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