Solution - Finding the midpoint between two points

The midpoint between the 2 points is:

(- 21, 13.5)

(-21,13.5)

See steps

Step-by-step explanation

1. Plot the two points and calculate the midpoint using the formula

The coordinates of Point 1 are:
$P_{1} (X_{1} = - 31, Y_{1} = - 34)$

The coordinates of Point 2 are:
$P_{2} (X_{2} = - 11, Y_{2} = 61)$

Pm represents the midpoint of the two points.

Use the X values in the midpoint formula to find the midpoint's X:

$X_{m} = (X_{1} + X_{2}) / 2$

$X_{1} = - 31$

$X_{m} = (- 31 + X_{2}) / 2$

$X_{2} = - 11$

$X_{m} = (- 31 + - 11) / 2$

Simplify the arithmetic

$X_{m} = (- 42) / 2$

$X_{m} = - 21$

Use the Y values in the midpoint formula to find the midpoint's Y:

$Y_{m} = (Y_{1} + Y_{2}) / 2$

$Y_{1} = - 34$

$Y_{m} = (- 34 + Y_{2}) / 2$

$Y_{2} = 61$

$Y_{m} = (- 34 + 61) / 2$

Simplify the arithmetic

$Y_{m} = (27) / 2$

$Y_{m} = 13.5$

And so, the midpoint is: $(- 21, 13.5)$

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Why learn this

Whether it's a carpenter building a seesaw, a contractor attaching a support beam to the middle of a bridge, or an eager traveler wanting to split a road trip into two days, people from many different walks of life benefit from knowing how to find the midpoint of two points. There is exactly one line between any two points and plugging the coordinates of these two points into the midpoint formula allows us to find the coordinates of the midpoint between them. This allows us to solve a wide range of real world problems and understand the relationships between objects and spaces around them.

Terms and topics

Midpoint of two points

Solution - Finding the midpoint between two points

Step-by-step explanation

1. Plot the two points and calculate the midpoint using the formula

Why learn this

Terms and topics

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