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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 #9 : Midpoint Formula

What is the midpoint of a line that connects the points (1,5) $\displaystyle (1,5)$ and (-7,9) $\displaystyle (-7,9)$ ?

Possible Answers:

(-3,7) $\displaystyle (-3,7)$

(-3,2) $\displaystyle (-3,2)$

(-4,7) $\displaystyle (-4,7)$

(-4,-2) $\displaystyle (-4,-2)$

(4,2) $\displaystyle (4,2)$

Correct answer:

(-3,7) $\displaystyle (-3,7)$

Explanation:

The midpoint formula is $\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$ $\displaystyle \left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$ .

Therefore, all we need to do is plug in the points given to us to find the midpoint.

In this case, $x_{1}=1,x_{2}=-7,y_{1}=5,y_{2}=9$ $\displaystyle x_{1}=1,x_{2}=-7,y_{1}=5,y_{2}=9$ .

To find the $\displaystyle x$ -value for the midpoint, we add: $\displaystyle 1+(-7)=1-7=-6$ . Then we divide by $\displaystyle 2$ : -6/2=-3 $\displaystyle -6/2=-3$ .

To find the $\displaystyle y$ -value for the midpoint, we add: 5+9=14 $\displaystyle 5+9=14$ . Then we divide by $\displaystyle 2$ : 14/2=7 $\displaystyle 14/2=7$ .

So our solution is (-3,7) $\displaystyle (-3,7)$ .

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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) $\displaystyle (4, 5)$

$\displaystyle (-3, -4)$

$\left(\frac{3}{2}, 1\right)$ $\displaystyle \left(\frac{3}{2}, 1\right)$

$\left(1, \frac{3}{2}\right)$ $\displaystyle \left(1, \frac{3}{2}\right)$

(2, 3) $\displaystyle (2, 3)$

Correct answer:

$\left(1, \frac{3}{2}\right)$ $\displaystyle \left(1, \frac{3}{2}\right)$

Explanation:

When finding the midpoint between two points, we use the midpoint formula

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

where $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ are the points given.

Knowing this, we can substitute the values into the formula. We get

$\left(\frac{3 + -1}{2}, \frac{4 + - 1}{2}\right)$ $\displaystyle \left(\frac{3 + -1}{2}, \frac{4 + - 1}{2}\right)$

$\left(\frac{3-1}{2}, \frac{4-1}{2}\right)$ $\displaystyle \left(\frac{3-1}{2}, \frac{4-1}{2}\right)$

$\left(\frac{2}{2}, \frac{3}{2}\right)$ $\displaystyle \left(\frac{2}{2}, \frac{3}{2}\right)$

$\left(1, \frac{3}{2}\right)$ $\displaystyle \left(1, \frac{3}{2}\right)$

Therefore, $\left(1, \frac{3}{2}\right)$ $\displaystyle \left(1, \frac{3}{2}\right)$ is the midpoint.

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Example Question #661 : Equations Of Lines

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Write the midpoint formula.

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

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

Substitute the given points.

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

Simplify the coordinate.

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

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

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Example Question #611 : Sat Subject Test In Math I

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

Possible Answers:

$\small (10,14)$ $\displaystyle \small (10,14)$

$\small (5,1)$ $\displaystyle \small (5,1)$

$\small (3,7)$ $\displaystyle \small (3,7)$

$\small (5,7)$ $\displaystyle \small (5,7)$

$\small (3,1)$ $\displaystyle \small (3,1)$

Correct answer:

$\small (5,7)$ $\displaystyle \small (5,7)$

Explanation:

The midpoint formula says that:

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

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

Plug the values into the formula and reduce:

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

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Example Question #11 : Midpoint Formula

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

Possible Answers:

(-1,-2) $\displaystyle (-1,-2)$

(1,2) $\displaystyle (1,2)$

(1,1) $\displaystyle (1,1)$

(-1,4) $\displaystyle (-1,4)$

(1,-2) $\displaystyle (1,-2)$

Correct answer:

(1,-2) $\displaystyle (1,-2)$

Explanation:

Write the formula for the midpoint.

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

Substitute the point into the formula.

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

The answer is: (1,-2) $\displaystyle (1,-2)$

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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 #661 : Equations Of Lines

Example Question #611 : Sat Subject Test In Math I

Example Question #11 : Midpoint Formula

All SAT II Math I Resources

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