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SAT Math : Geometry

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Example Questions

Example Question #4 : Midpoint Formula

What is the midpoint between (1,4) and (5,12) ?

Possible Answers:

(8,2)

(2,10)

(4,8)

(3,6)

(3,8)

Correct answer:

(3,8)

Explanation:

The midpoint is the point halfway between the two endpoints, so sum up the coordinates and divide by 2:

$(\frac{1+5}{2},\frac{4+12}{2})=(\frac{6}{2},\frac{16}{2})=(3,8)$

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Example Question #2 : How To Find The Midpoint Of A Line Segment

$\overline{AB}$ has endpoints A(4,1) and B(7,12) .

What is the midpoint of $\overline{AB}$ ?

Possible Answers:

(4,12)

(5,6)

(5.5, 6.5)

(6,5)

(6.5,5.5)

Correct answer:

(5.5, 6.5)

Explanation:

The midpoint is simply the point halfway between the x-coordinates and halfway between the y-coordinates:

Sum the x-coordinates and divide by 2:

4+7=11

$11\div 2=5.5$

Sum the y-coordinates and divide by 2:

1+12=13

$13\div 2=6.5$

Therefore the midpoint is (5.5, 6.5).

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

What is the mid point of a linear line segment that spans from (-2,4) to (5,14) ?

Possible Answers:

(5,8)

(1,-3)

(-3.5, -5)

(4,5)

(1.5,9)

Correct answer:

(1.5,9)

Explanation:

To find the midpoint of a line segment, use this formula:

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

Therefore, the midpoint of the given line segment is:

$\left ( \frac{-2+5}{2}\right ),\left ( \frac{4+14}{2} \right )$

(1.5, 9)

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

Find the midpoint of the line segment with endpoints (1,3) and (5,7).

Possible Answers:

5,3

(-2,-2)

(3,5)

(2,2)

Correct answer:

(3,5)

Explanation:

To solve, simply use the midpoint formula as outlined below.

Given,

(x_1,y_1)=(1,3); (x_2,y_2)=(5,7)

Thus,

$midpoint=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{1+5}{2},\frac{3+7}{2}\right)=(3,5)$

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Example Question #2 : How To Find The Midpoint Of A Line Segment

Find the midpoint of a line segment with end points (1,3) and (11,3).

Possible Answers:

(6,9)

(4,8)

(5,3)

(6,3)

Correct answer:

(6,3)

Explanation:

To solve, simply realize you are on a horizantal line, so you just need to find the distance betweent he two x coordants and find half way between them. Thus,

11-1=10

$\frac{10}{2}=5$

Thus, the midpoint is at (1+5,3) which is (6,3).

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Example Question #11 : Midpoint Formula

What is the midpoint of a line segment that begins at (0, -1) and ends at (4, 10)?

Possible Answers:

(2, 5)

(2, 10)

(2, 4)

None of the given answers.

$(2, \frac{9}{2})$

Correct answer:

$(2, \frac{9}{2})$

Explanation:

The midpoint of a line segment can be found by averaging the x-values and y-values of the given ordered pairs. In other words,

$M=(\frac{x_{1}+x_2}{2}, \frac{y_1+y_2}{2})$ .

Take the average of the given x- and y-values of our ordered pairs.

$M=(\frac{0+4}{2}, \frac{-1+10}{2})=(2, \frac{9}{2})$

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Example Question #12 : Midpoint Formula

Find the midpoint between the point (1.25, 2.5) and the center of the given circle.

(x-0.75)^2 + (y-0.5)^2 = 4

Possible Answers:

(0.25, 1)

(1, 1)

None of the given answers

(1, 1.5)

(0.75, 0.75)

Correct answer:

(1, 1.5)

Explanation:

Remember that the general equation for a circle with center (h, k) and radius is (x-h)^2 + (y-k)^2 = r^2 .

With this in mind, the center of our circle is (0.75, 0.5) .

To find the midpoint between our two points, use the midpoint formula.

$M = (\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2}) = (\frac{0.75+1.25}{2}, \frac{0.5+2.5}{2}) = (\frac{2}{2}, \frac{3}{2}) = (1, 1.5)$

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Example Question #13 : Midpoint Formula

The following coordinates represent the vertices of a box. Where does the center of the box lie?

(1, 1), (1, 9), (9, 9), (9,1)

Possible Answers:

(-8, -8)

None of the given answers

(4, 4)

(5, 5)

(8, 8)

Correct answer:

(5, 5)

Explanation:

To solve this, we need to choose two points that lie diagonally across from each other. Let's use (1,9) and (9, 9) . Now, we can substitute these points into the Midpoint Formula.

$M = (\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2}) = (\frac{9+1}{2}, \frac{9+1}{2}) = (\frac{10}{2}, \frac{10}{2}) = (5, 5)$

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Example Question #14 : Midpoint Formula

Give the coordinates of the midpoint, in terms of , of a segment on the coordinate plane whose endpoints are $\left (0.4 , N \right )$ and $\left ( N, -0.4 \right )$ .

Possible Answers:

(0.5 N + 0.2,0.5 N + 0.2)

(0.5 N - 0.2,0.5 N + 0.2)

(0.5 N - 0.2,0.5 N - 0.2)

(0,0)

(0.5 N + 0.2,0.5 N - 0.2)

Correct answer:

(0.5 N + 0.2,0.5 N - 0.2)

Explanation:

The coordinates $(x_{M}, y_{M})$ of the midpoint of the line segment with endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ can be calculated using the formulas

$x_{M} =\frac{ x_{1} + x_{2} }{2}$

and

$y_{M} =\frac{ y_{1} + y_{2} }{2}$ .

Setting $x_{1} = 0.4$ and $x_{2} =N$ , and substituting:

$x_{M} =\frac{ 0.4 + N }{2} = \frac{ N }{2} + \frac{ 0.4 }{2} = 0.5 N + 0.2$

Setting $y_{1} =N$ and $y_{2} = -0.4$ , and substituting:

$x_{M} =\frac{N + (-0.4) }{2} = \frac{ N }{2} - \frac{ 0.4 }{2} = 0.5 N - 0.2$

The coordinates of the midpoint, in terms of , are

(0.5 N + 0.2,0.5 N - 0.2)

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Example Question #12 : How To Find The Midpoint Of A Line Segment

The two endpoints of a line segment are (1, 7) and (5, 3) . Find the midpoint.

Possible Answers:

(6, 3)

(3, 5)

(4, 3)

(-5, 3)

(5, 3)

Correct answer:

(3, 5)

Explanation:

In order to find the midpoint of a line segment, you need to average the x and y values of the endpoints.

The midpoint formula is

$((x_{1}+x_{2})/2), ((y_{1}+y_{2})/2)$

After plugging in the values you get

(1 + 5) / 2 for x

and (7 + 3) / 2 for y

Therefore, the midpoint is at (3, 5) .

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SAT Math : Geometry

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #4 : Midpoint Formula

Example Question #2 : How To Find The Midpoint Of A Line Segment

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

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

Example Question #2 : How To Find The Midpoint Of A Line Segment

Example Question #11 : Midpoint Formula

Example Question #12 : Midpoint Formula

Example Question #13 : Midpoint Formula

Example Question #14 : Midpoint Formula

Example Question #12 : How To Find The Midpoint Of A Line Segment

All SAT Math Resources

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