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Algebra 1 : Equations of Lines

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Example Questions

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 #888 : Functions And Lines

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

Possible Answers:

(1,3)

(1,4)

(4,1)

(3,1)

(3,7)

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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Example Question #891 : Functions And Lines

Two points, (1,2) and (2,5) , are connected to form a line. What is the midpoint?

Possible Answers:

$(\frac{3}{2},\frac{7}{2})$

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

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

$(\frac{1}{2},\frac{7}{2})$

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

Correct answer:

$(\frac{3}{2},\frac{7}{2})$

Explanation:

Write the midpoint formula. The midpoint is the center of the line segment.

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

Substitute the values of the coordinates.

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) = (\frac{1+2}{2},\frac{2+5}{2})=(\frac{3}{2},\frac{7}{2})$

The midpoint is: $(\frac{3}{2},\frac{7}{2})$

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Example Question #641 : Equations Of Lines

Find the midpoint of the line segment formed by the points

(-1, -3) and (3, 3).

Possible Answers:

(2, 2)

(2, 0)

(1, -1)

(1, 0)

(-4, -6)

Correct answer:

(1, 0)

Explanation:

To find the midpoint between two points, we use the following formula:

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

where (x_1, y_1) and (x_2, y_2) are the points given. So, given the points

(-1, -3) and (3, 3), we can substitute into the formula.

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

$(\frac{2}{2}, \frac{0}{2})$

(1, 0)

Therefore, the midpoint between (-1, -3) and (3, 3) is (1, 0).

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Example Question #893 : Functions And Lines

Find the midpoint of a line segment with the following endpoints:

(2,6)(12,12)

Possible Answers:

(14,18)

(7,9)

(12,6)

(6,8)

Correct answer:

(7,9)

Explanation:

Finding the midpoint of a line segment only requires that we find the midpoint, or average of both the x and y components. In order to do that, we use the following formula:

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

For the points (2,6) and (12,12) plug in the numbers and solve:

$(\frac{2+12}{2},\frac{6+12}{2})=(\frac{14}{2},\frac{18}{2})=(7,9)$

This gives a final answer of (7,9)

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Example Question #894 : Functions And Lines

Find the midpoint of the line segment with the following endpoints:

(-2,5)(4,7)

Possible Answers:

(6,1)

(1,6)

(3,5)

(8,9)

Correct answer:

(1,6)

Explanation:

Finding the midpoint of a line segment only requires that we find the midpoint, or average of both the x and y components. In order to do that, we use the following formula:

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

For the points (-2,5) and (4,7) plug in the numbers and solve:

$(\frac{-2+4}{2},\frac{5+7}{2})=(\frac{2}{2},\frac{12}{2})=(1,6)$

This gives a final answer of (1,6)

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Example Question #895 : Functions And Lines

Find the midpoint of the line segment with the following endpoints:

(15,5)(3,5)

Possible Answers:

(6,5)

(9,5)

(9,0)

(12,5)

Correct answer:

(9,5)

Explanation:

Finding the midpoint of a line segment only requires that we find the midpoint, or average of both the x and y components. In order to do that, we use the following formula:

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

For the points (15,5) and (3,5) plug in the numbers and solve:

$(\frac{15+3}{2},\frac{5+5}{2})=(\frac{18}{2},\frac{10}{2})=(9,5)$

This gives a final answer of (9,5)

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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #886 : Functions And Lines

Example Question #9 : Midpoint Formula

Example Question #887 : Functions And Lines

Example Question #888 : Functions And Lines

Example Question #889 : Functions And Lines

Example Question #891 : Functions And Lines

Example Question #641 : Equations Of Lines

Example Question #893 : Functions And Lines

Example Question #894 : Functions And Lines

Example Question #895 : Functions And Lines

All Algebra 1 Resources

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