Question

What is the formula for calculating midpoint​

Answer 1

MIDPOINT

The intersection of a line segment's two endpoints is known as the midpoint. From the midpoint to one endpoint and the midpoint to the other endpoint, you will be given two equal distances.

The formula for calculating the midpoint is given below:

• 
  `\boxed{ \bold{ \: \: M = \bigg((x_1 + x_2)/(2), (y_1 + y_2)/(2)\bigg) \: \: }}`

For example, let us try solving this sample problem below using the midpoint formula:

Sample problem: A new transmission tower will be put up midway between two existing towers. On a map drawn on a coordinate plane, the coordinates of first existing tower are (-5, -3) and the coordinates of the second existing tower are (9, 13). What are the coordinates of the point where the new tower will be placed?

From inspection on the given problem:

• 
  `\sf (x_1, y_1) = (-5, -3)`
• 
  `\sf (x_2, y_2) = (9, 13)`

Substitute the given values into the midpoint formula and solve for M:

• 
  `\sf M = \bigg((x_1 + x_2)/(2), (y_1 + y_2)/(2)\bigg)`

• 
  `\sf M = \bigg((-5 + 9)/(2), (-3 + 13)/(2)\bigg)`

• 
  `\sf M = \bigg((4)/(2), (10)/(2)\bigg)`

• 
  `\sf M = (2, 5)`

Therefore, the coordinates of the point are (2, 5).

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Now, wasn't that easy? Try this other sample problem:

• The endpoints of a segment are (-5, 2) and (9, 12), respectively. What are the coordinates of its midpoint?

From the sample problem above, you may solve it on your own to enhance your skill on calculating the midpoint.

Cheers!