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SAT II Math I : Coordinate Geometry

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

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

Example Questions

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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Example Question #661 : Equations Of Lines

A line is connected by points (2,5) and (-1,3) on a graph. What is the midpoint?

Possible Answers:

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

$(\frac{9}{2},4)$

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

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

$(\frac{1}{2},4)$

Correct answer:

$(\frac{1}{2},4)$

Explanation:

Write the midpoint formula.

$(x,y) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Let (x_1,y_1) = (2,5) and (x_2,y_2) = (-1,3) .

Substitute the given points.

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

Simplify the coordinate.

$(x,y) =(\frac{1}{2},4)$

The answer is: $(\frac{1}{2},4)$

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Example Question #11 : Midpoint Formula

Find the midpoint between (2,8) and (8,6).

Possible Answers:

$\small (3,1)$

$\small (5,7)$

$\small (10,14)$

$\small (5,1)$

$\small (3,7)$

Correct answer:

$\small (5,7)$

Explanation:

The midpoint formula says that:

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

Given (2,8) and (8,6); $\small x_{1}=2$ $\small \small x_{2}=8$ $\small \small y_{1}=8$ $\small \small y_{2}=6$

Plug the values into the formula and reduce:

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})=(\frac{2+8}{2},\frac{8+6}{2})=(5,7)$

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Example Question #612 : Sat Subject Test In Math I

Find the midpoint between (-1,-3) and (3,-1) .

Possible Answers:

(1,2)

(1,-2)

(1,1)

(-1,-2)

(-1,4)

Correct answer:

(1,-2)

Explanation:

Write the formula for the midpoint.

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

Substitute the point into the formula.

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

The answer is: (1,-2)

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All SAT II Math I Resources

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SAT II Math I : Coordinate Geometry

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

All SAT II Math I Resources

Example Questions

Example Question #2 : Midpoint Formula

Example Question #614 : Equations Of Lines

Example Question #9 : Midpoint Formula

Example Question #10 : Midpoint Formula

Example Question #661 : Equations Of Lines

Example Question #11 : Midpoint Formula

Example Question #612 : Sat Subject Test In Math I

All SAT II Math I Resources

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