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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

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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 #87 : Midpoint Formula

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

Possible Answers:

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

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

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

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

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

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:

$\small (5,7)$

$\small (10,14)$

$\small (5,1)$

$\small (3,7)$

$\small (3,1)$

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 #181 : Geometry

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

Possible Answers:

(-1,-2)

(-1,4)

(1,2)

(1,-2)

(1,1)

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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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 #9 : Midpoint Formula

Example Question #10 : Midpoint Formula

Example Question #87 : Midpoint Formula

Example Question #11 : Midpoint Formula

Example Question #181 : Geometry

All SAT II Math I Resources

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