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Algebra 1 : Functions and Lines

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Example Questions

Example Question #44 : How To Find The Midpoint Of A Line Segment

Find the midpoint of the given set of coordinates:

$(-5,2)\,and\, (3,-4)$

Possible Answers:

(1,3)

(-1,-1)

(4,-1)

(1,-3)

(-2,-2)

Correct answer:

(-1,-1)

Explanation:

To find the midpoint, we must plug in the values for both points into the midpoint formula:

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})=(\frac{-5+3}{2},\frac{2+-4}{2})=(\frac{-2}{2},\frac{-2}{2})=(-1,-1)$

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Example Question #882 : Functions And Lines

What is the midpoint of a line segment with the end points (1,2) and (7,8) ?

Possible Answers:

(-5,-4)

(2,1)

(3,3)

(4,5)

(5,4)

Correct answer:

(4,5)

Explanation:

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{1+7}{2},\frac{2+8}{2})$

$midpoint=(\frac{8}{2},\frac{10}{2})$

$midpoint={\color{Blue} (4,5)}$

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Example Question #883 : Functions And Lines

Find the midpoint of a line segment with (0,0) and (10,4) as its endpoints.

Possible Answers:

(5,4)

(2,5)

(-5,-2)

(-5,-4)

(5,2)

Correct answer:

(5,2)

Explanation:

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{0+10}{2},\frac{0+4}{2})$

$midpoint=(\frac{10}{2},\frac{4}{2})$

$midpoint={\color{Blue} (5,2)}$

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Example Question #884 : Functions And Lines

A line segment has the endpoints (20,40) and (100,26) . What's the midpoint of the line segment?

Possible Answers:

(33,60)

(60,33)

(120,66)

(80,72)

(60,43)

Correct answer:

(60,33)

Explanation:

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{20+100}{2},\frac{40+26}{2})$

$midpoint=(\frac{120}{2},\frac{66}{2})$

$midpoint={\color{Blue} (60,33)}$

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Example Question #885 : Functions And Lines

What is the midpoint of a line segment AB is A is at (3,4) and B is at (17,2) ?

Possible Answers:

(10,5)

(13,7)

(7,-2)

(10,3)

(-7,2)

Correct answer:

(10,3)

Explanation:

This kind of problem can be quickly solved for by using the midpoint formula:

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ where (x₁,y₁) and (x₂,y₂). Either of the endpoints may be assigned as either coordinate point.

Substituting in the information,

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

$\left(\frac{3+17}{2}, \frac{4+2}{2}\right)$

$\left(\frac{20}{2}, \frac{6}{2}\right)$

${\color{Blue} (10,3)}$

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Example Question #886 : Functions And Lines

Find the midpoint of a line segment with the endpoints $\small (-3,-12)$ and $\small (27,-30)$ .

Possible Answers:

$\small (-15,9)$

$\small (15,-9)$

$\small (-12,-21)$

$\small (16,10)$

$\small (12,-21)$

Correct answer:

$\small (12,-21)$

Explanation:

This kind of problem can be quickly solved for by using the midpoint formula:

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ where $\small (x_1,y_1)$ and $\small (x_2,y_2)$ . Either of the endpoints may be assigned as either coordinate point.

Substituting in the information,

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

$\left(\frac{-3+27}{2}, \frac{-30-12}{2}\right)$

$\left(\frac{24}{2}, \frac{-42}{2}\right)$

${\color{Blue} (12,-21)}$

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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 #887 : Functions And Lines

Find the midpoint of the line segment with the endpoints of (-2, 3) and (4, 1)

Possible Answers:

(2, 1)

(-1, -2)

(1, 2)

(-8, 3)

(2, 4)

Correct answer:

(1, 2)

Explanation:

To find the midpoint of a line segment, take the two endpoints and use the following formula:

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

Using this formula, we know

$(x_{1}, y_{1}) \text{ and } (x_{2}, y_{2})$

is the same as

$(-2, 3) \text{ and } (4,1)$

Using substitution, we get

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

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

(1, 2)

Therefore, the midpoint of the line segment formed by the endpoints $(-2, 3) \text{ and } (4,1)$ is (1, 2) .

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Example Question #51 : How To Find The Midpoint Of A Line Segment

Find the midpoint of the line segment with the following endpoints: $(0,1)\&(2,7)$ .

Possible Answers:

(1,3)

(4,1)

(1,4)

(3,7)

(3,1)

Correct answer:

(1,4)

Explanation:

To find the midpoint of this segment, we plug the values of our respective coordinates into the midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$\left(\frac{0+2}{2},\frac{7+1}{2}\right)$

Simplify.

(1,4)

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Example Question #889 : Functions And Lines

Find the point located exactly halfway between the points and

Possible Answers:

(3,27)

(27,3)

(-3,-27)

(-27,-3)

Correct answer:

(27,3)

Explanation:

Find the point located exactly halfway between the points and

We can find the midpoint of any pair of points via the following:

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

All we need to do is plug in our given points.

We'll call point 2 and point 1

So,

$M=(\frac{63-9}{2},\frac{43-37}{2})=(\frac{54}{2},\frac{6}{2})=(27,3)$

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #44 : How To Find The Midpoint Of A Line Segment

Example Question #882 : Functions And Lines

Example Question #883 : Functions And Lines

Example Question #884 : Functions And Lines

Example Question #885 : Functions And Lines

Example Question #886 : Functions And Lines

Example Question #9 : Midpoint Formula

Example Question #887 : Functions And Lines

Example Question #51 : How To Find The Midpoint Of A Line Segment

Example Question #889 : Functions And Lines

All Algebra 1 Resources

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