Midpoint Formula

SAT Subject Test in Math II · Learn by Concept

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SAT Subject Test in Math II › Midpoint Formula

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1

What is the coordinates of the point exactly half way between (-2, -3) and (5, 7)?

$\left(\frac{3}{2}, 2\right)$

CORRECT

$\left(2, \frac{-3}{2}\right)$

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Explanation

We need to use the midpoint formula to solve this question.

$midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In our case

and

Therefore, substituting these values in we get the following:

$midpoint=(\frac{-2+5}{2}, \frac{-3+7}{2})$

$midpoint= (\frac{3}{2}, \frac{4}{2})$

$(\frac{3}{2}, 2)$

2

Find the point halfway between points A and B.

CORRECT

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Explanation

Find the point halfway between points A and B.

We are going to need to use midpoint formula. If you ever have difficulty recalling midpoint formula, try to recall that it is basically taking two averages. One average is the average of your x values, the other average is the average of your y values.

$Mid=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Now we plug and chug!

$Mid=(\frac{19+67}{2},\frac{54+34}{2})=(\frac{86}{2},\frac{88}{2})=(43,44)$

So our answer is (43,44)

3

Find the midpoint between and .

$(\frac{1}{2}, 6)$

CORRECT

$(\frac{1}{2}, -3)$

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$(\frac{3}{2}, -3)$

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$(\frac{3}{2}, 3)$

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$(\frac{1}{2}, -6)$

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Explanation

Write the midpoint formula.

$M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Substitute the points.

$M = (\frac{2+(-1)}{2}, \frac{3+9}{2}) = (\frac{1}{2}, 6)$

The answer is: $(\frac{1}{2}, 6)$

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