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SAT II Math II : Midpoint Formula

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #131 : Geometry

Find the point halfway between points A and B.

$\displaystyle A=(19,54)$

$\displaystyle B=(67,34)$

Possible Answers:

(43,44) $\displaystyle (43,44)$

(44,43) $\displaystyle (44,43)$

(86,88) $\displaystyle (86,88)$

(42,45) $\displaystyle (42,45)$

Correct answer:

(43,44) $\displaystyle (43,44)$

Explanation:

Find the point halfway between points A and B.

$\displaystyle A=(19,54)$

$\displaystyle B=(67,34)$

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.

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

Now we plug and chug!

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

So our answer is (43,44)

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Example Question #1 : Midpoint Formula

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

Possible Answers:

(3,-2) $\displaystyle (3,-2)$

(2, -3) $\displaystyle (2, -3)$

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

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

Correct answer:

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

Explanation:

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

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

In our case $\displaystyle (x_1, y_1)=(-2,-3)$

and $\displaystyle (x_2, y_2)=(5,7)$

Therefore, substituting these values in we get the following:

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

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

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

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Example Question #1 : Midpoint Formula

Find the midpoint between (2,3) $\displaystyle (2,3)$ and (-1,9) $\displaystyle (-1,9)$.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Write the midpoint formula.

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

Substitute the points.

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

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

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All SAT II Math II Resources

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SAT II Math II : Midpoint Formula

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #131 : Geometry

Example Question #1 : Midpoint Formula

Example Question #1 : Midpoint Formula

All SAT II Math II Resources

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