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SAT II Math I : Geometry

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

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All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Distance Formula

Find the distance between (3, 4) and (-12, -5) .

Possible Answers:

$3 \sqrt {34}$

$2 \sqrt {6}$

$\sqrt {82}$

$10 \sqrt {3}$

Correct answer:

$3 \sqrt {34}$

Explanation:

For this problem we will need to use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

In our case,

(x_1,y_1)=(-12, -5) and (x_2,y_2)=(3, 4) .

Plugging these values into the formula we are able to find the distance.

$d = \sqrt {(3-(-12))^2 + (4-(-5)))^2))}$

$=\sqrt {15^2+9^2}$

$= \sqrt {306}$

$= \sqrt {9 \cdot 34} = 3 \sqrt {34}$

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Example Question #2 : Distance Formula

What is the distance between (1,6) and (-3,-2) ?

Possible Answers:

$4\sqrt2$

$\frac{4}{3}$

$2\sqrt5$

$5\sqrt4$

$4\sqrt5$

Correct answer:

$4\sqrt5$

Explanation:

Write the distance formula.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the points:

(x_1,y_1)=(1,6)

(x_2,y_2)=(-3,-2)

$d=\sqrt{(-3-1)^2+(-2-6)^2}$

$d=\sqrt{16+64} = \sqrt{80}$

The radical can be broken down into factors of perfect squares.

$\sqrt{80} = \sqrt{16}\cdot \sqrt5 = 4\sqrt5$

The answer is: $4\sqrt5$

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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:

(7,13)

(1.5,7.5)

(8,12)

(6,13.5)

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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SAT II Math I : Geometry

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

All SAT II Math I Resources

Example Questions

Example Question #1 : Distance Formula

Example Question #2 : Distance Formula

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

All SAT II Math I Resources

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