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SAT II Math I : Midpoint Formula

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Example Questions

Example Question #1 : Midpoint Formula

Find the midpoint of the line that passes through the points (-1,4) and (5,2) .

Possible Answers:

(2,-3)

(3,3)

(2,3)

(3,-2)

(-3,2)

Correct answer:

(2,3)

Explanation:

Recall the midpoint formula as $(\frac{x1+x2}{2}, \frac{y1+y2}{2})$ .

Thus,

$(\frac{-1+5}{2},\frac{4+2}{2}) = (2,3)$

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Example Question #2 : Midpoint Formula

Find the midpoint of the line that passes through the points (2,-1) and (-2,1) .

Possible Answers:

(2,-1)

(-2,-1)

(0,0)

(2,1)

(-2,1)

Correct answer:

(0,0)

Explanation:

Recall the midpoint formula as $(\frac{x1+x2}{2}, \frac{y1+y2}{2})$ .

Thus,

$(\frac{2+(-2)}{2},\frac{-1+1}{2}) = (0,0)$

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Example Question #2 : Midpoint Formula

What is the midpoint between $\left ( 2,3\right )$ and $\left ( -7,4\right )$ ?

Possible Answers:

(-5,-7)

$\left(\frac{-5}{2}, \frac{7}{2}\right)$

(7,5)

(-5,7)

Correct answer:

$\left(\frac{-5}{2}, \frac{7}{2}\right)$

Explanation:

The formula to find the midpoint is as follows:

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

In our case our (x_1, y_1)= (2, 3)

our (x_2, y_2)=(-7, 4)

substituting in these values we get

midpoint = $\left(\frac{2+-7}{2}, \frac{3+4}{2}\right)=\left(\frac{-5}{2}, \frac{7}{2}\right)$

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Example Question #4 : Midpoint Formula

What is the midpoint between $\left ( 1,3\right )$ and $\left ( 5,9\right )$ ?

Possible Answers:

$\left ( 1,5\right )$

$\left ( 1,9\right )$

$\left ( 3,9\right )$

$\left ( 3,5\right )$

$\left ( 3,6\right )$

Correct answer:

$\left ( 3,6\right )$

Explanation:

To find the midpoint of two points you find the average of both the values and values.

For ,

$\frac{1+5}{2}=3$ .

For ,

$\frac{3+9}{2}=6$ .

This means the midpoint is $\left ( 3,6\right )$ .

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Example Question #1 : How To Find The Midpoint Of A Line Segment

What is the midpoint of the points (3,12) and (9,15)?

Possible Answers:

(8,12)

(6,13.5)

(7,13)

(1.5,7.5)

Correct answer:

(6,13.5)

Explanation:

To find the midpoint we must know the midpoint formula which is

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

We then take the -coordinate from the first point and plug it into the formula as $x_{1}$ .

We take the -coordinate from the second point and plug it into the formula as $x_{2}$ .

We then do the same for $y_{1}$ and $y_{2}$ .

With all of the points plugged in our equation will look like this.

$(\frac{3+9}{2},\frac{12+15}{2})$

We then perform the necessary addition and division to get the answer of

$(\frac{12}{2},\frac{27}{2})=(6,13.5)$

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Example Question #3 : How To Find The Midpoint Of A Line Segment

Find the midpoint of the line segment that connects the two points below.

Point 1: (0,-3)

Point 2: (-2, 4)

Possible Answers:

$(-1, \frac{7}{2})$

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

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

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

$(1, -\frac{7}{2})$

Correct answer:

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

Explanation:

The average of the the -coordinates and the average of the y-coordinates of the given points will give you the mid-point of the line that connects the points.

$\textup{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ , where (x_1,y_1) is (0,-3) and (x_2,y_2) is (-2, 4) .

$(\frac{(0)+(-2)}{2}, \frac{(-3)+(4)}{2})$

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

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

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Example Question #2 : Midpoint Formula

Find the midpoint of the line segment with endpoints (3.6, 9.1) and (7.2, -1.5) .

Possible Answers:

$\left (1.8, -5.3 \right )$

$\left (-1.8, 5.3 \right )$

(3.8, 5.4)

(5.4, 3.8)

$\left (6.35, 2.85 \right )$

$\left (-1.8, 5.3 \right )$

$\left (1.8, -5.3 \right )$

$\left (6.35, 2.85 \right )$

Correct answer:

(5.4, 3.8)

Explanation:

Use the midpoint formula:

$\left ( \frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}} \right )$

Substitute:

$\frac{x_{1}+x_{2}}{2} =\frac{3.6+7.2}{2} = \frac{10.8}{2} = 5.4$

$\frac{y_{1}+y_{2}}{2}} \right = \frac{9.1+(-1.5)}{2}} = \frac{7.6}{2} = 3.8$

The midpoint is (5.4, 3.8)

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Example Question #614 : Equations Of Lines

Find the midpoint of the line segment with these endpoints: (5, 7) and (9, 15) .

Possible Answers:

(8, 12)

(4, 8)

(7, 11)

(14, 22)

Correct answer:

(7, 11)

Explanation:

The midpoint formula is

$\left(\frac{x_{1}+x_{2}}2,\frac{y_{1}+y_2}{2}\right)$ .

Add the two values together and divide the total by two to find the value of the midpoint. Add the two values together and divide the total by two to find the value of the midpoint.

$\\ \left(\frac{5+9}2,\frac{7+15}{2}\right)\\ \\=\left(\frac{14}{2},\frac{22}{2} \right )\\ \\=(7,11)$

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Example Question #9 : Midpoint Formula

What is the midpoint of a line that connects the points (1,5) and (-7,9) ?

Possible Answers:

(-3,7)

(-3,2)

(-4,7)

(-4,-2)

(4,2)

Correct answer:

(-3,7)

Explanation:

The midpoint formula is $\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$ .

Therefore, all we need to do is plug in the points given to us to find the midpoint.

In this case, $x_{1}=1,x_{2}=-7,y_{1}=5,y_{2}=9$ .

To find the -value for the midpoint, we add: 1+(-7)=1-7=-6 . Then we divide by : -6/2=-3 .

To find the -value for the midpoint, we add: 5+9=14 . Then we divide by : 14/2=7 .

So our solution is (-3,7) .

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Example Question #10 : Midpoint Formula

Find the midpoint of a line with the endpoings (3, 4) and (-1, -1).

Possible Answers:

(4, 5)

(-3, -4)

$\left(\frac{3}{2}, 1\right)$

$\left(1, \frac{3}{2}\right)$

(2, 3)

Correct answer:

$\left(1, \frac{3}{2}\right)$

Explanation:

When finding the midpoint between two points, we use the midpoint formula

$\left(\frac{x_1 + x_2}{2}, \frac{y_1+y_2}{2}\right)$

where (x_1, y_1) and (x_2, y_2) are the points given.

Knowing this, we can substitute the values into the formula. We get

$\left(\frac{3 + -1}{2}, \frac{4 + - 1}{2}\right)$

$\left(\frac{3-1}{2}, \frac{4-1}{2}\right)$

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

$\left(1, \frac{3}{2}\right)$

Therefore, $\left(1, \frac{3}{2}\right)$ is the midpoint.

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SAT II Math I : Midpoint Formula

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

All SAT II Math I Resources

Example Questions

Example Question #1 : Midpoint Formula

Example Question #2 : Midpoint Formula

Example Question #2 : Midpoint Formula

Example Question #4 : Midpoint Formula

Example Question #1 : How To Find The Midpoint Of A Line Segment

Example Question #3 : How To Find The Midpoint Of A Line Segment

Example Question #2 : Midpoint Formula

Example Question #614 : Equations Of Lines

Example Question #9 : Midpoint Formula

Example Question #10 : Midpoint Formula

All SAT II Math I Resources

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