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SAT Math : Coordinate Geometry

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Example Questions

Example Question #1 : Midpoint Formula

Find the coordinates for the midpoint of the line segment that spans from (1, 1) to (11, 11).

Possible Answers:

(5, 5)

(6, 6)

(7, 7)

(5, 6)

(6, 5)

Correct answer:

(6, 6)

Explanation:

The correct answer is (6, 6). The midpoint formula is ((x₁+ x₂)/2),((y₁+ y₂)/2) So 1 + 11 = 12, and 12/2 = 6 for both the x and y coordinates.

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

What is the midpoint between the points (–1, 2) and (3, –6)?

Possible Answers:

(1,–2)

(3,1)

(–2,–1)

(1,2)

(–1,2)

Correct answer:

(1,–2)

Explanation:

midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

= ((–1 + 3)/2, (2 – 6)/2)

= (2/2, –4/2)

= (1,–2)

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

A line segment connects the points $(-1,4)$ and $(3,16)$ . What is the midpoint of this segment?

Possible Answers:

$(2,10)$

$(-1,6)$

$(1,10)$

$(0,6)$

$(2,5)$

Correct answer:

$(1,10)$

Explanation:

To solve this problem you will need to use the midpoint formula:

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

Plug in the given values for the endpoints of the segment: $(-1,4)$ and $(3,16)$ .

$midpoint = (\frac{-1+3}{2},\frac{4+16}{2} ) = (\frac{2}{2}, \frac{20}{2}) = (1, 10)$

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Example Question #2 : Midpoint Formula

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

Possible Answers:

(8,2)

(4,8)

(2,10)

(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 #3 : 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:

(5,6)

(6.5,5.5)

(4,12)

(6,5)

(5.5, 6.5)

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, 10)

(2, 4)

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

None of the given answers.

(2, 5)

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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SAT Math : Coordinate Geometry

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Midpoint Formula

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 #2 : Midpoint Formula

Example Question #3 : 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

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