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Algebra 1 : Equations of Lines

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Example Questions

Example Question #1 : Midpoint Formula

A line segment has the midpoint (-2,3) . One end point of the line segment is located at (5,6) . What is the other end point?

Possible Answers:

(-9,0)

(-1,12)

(1,12)

(9,0)

Correct answer:

(-9,0)

Explanation:

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

$(-2,3)=(\frac{5+x_2}{2},\frac{6+y_2}{2})$

$2(-2,3)=2(\frac{5+x_2}{2},\frac{6+y_2}{2})$

(-4,6)=(5+x_2,6+y_2)

(x_2,y_2)=(-4-5,6-6)

(x_2,y_2)=(-9,0)

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Example Question #2 : Midpoint Formula

Find the midpoint on the line segment from (2, 3) to (4, 1).

Possible Answers:

(–2, 2)

(3, 2)

(6, 4)

(2, 2)

(2, –2)

Correct answer:

(3, 2)

Explanation:

By using the midpoint formula, we can find the x and y coodinantes fo the midpoint.

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

$\frac{x_1+x_2}{2}=\frac{2+4}{2}=\frac{6}{2}=3$

$\frac{y_1+y_2}{2}=\frac{3+1}{2}=\frac{4}{2}=2$

Our coordinates are (3, 2).

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Example Question #1 : How To Find The Midpoint Of A Line Segment

Point X (2, 9) and Point Y (8, 3) are endpoints on a line segment. What is the Midpoint M of that line segment?

Possible Answers:

$\left ( 6,6 \right )$

$\left ( 6,7 \right )$

$\left ( -3,6 \right )$

$\left ( 2,8 \right )$

$\left ( 5,6 \right )$

Correct answer:

$\left ( 5,6 \right )$

Explanation:

To find the midpoint of a line segment, you add together the components and divide by two ( $\frac{2+8}{2}$ = 5) , do the same for ( $\frac{3+9}{2}$ =6). The answer is (5, 6).

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Example Question #32 : Coordinate Geometry

What is the midpoint of the points (3,12) and (9,15)?

Possible Answers:

(1.5,7.5)

(8,12)

(6,13.5)

(7,13)

Correct answer:

(6,13.5)

Explanation:

To find the midpoint we must know the midpoint formula which is

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

We then take the -coordinate from the first point and plug it into the formula as $x_{1}$ .

We take the -coordinate from the second point and plug it into the formula as $x_{2}$ .

We then do the same for $y_{1}$ and $y_{2}$ .

With all of the points plugged in our equation will look like this.

$(\frac{3+9}{2},\frac{12+15}{2})$

We then perform the necessary addition and division to get the answer of

$(\frac{12}{2},\frac{27}{2})=(6,13.5)$

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Example Question #3 : How To Find The Midpoint Of A Line Segment

Find the midpoint of the line segment that connects the two points below.

Point 1: (0,-3)

Point 2: (-2, 4)

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

The average of the the -coordinates and the average of the y-coordinates of the given points will give you the mid-point of the line that connects the points.

$\textup{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ , where (x_1,y_1) is (0,-3) and (x_2,y_2) is (-2, 4) .

$(\frac{(0)+(-2)}{2}, \frac{(-3)+(4)}{2})$

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

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

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Example Question #1 : How To Find The Midpoint Of A Line Segment

Find the midpoint that falls between (1,-7) and (13,3) .

Possible Answers:

(7,-2)

(14,-4)

(5,1)

(-7,2)

(-2,7)

Correct answer:

(7,-2)

Explanation:

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

When we plug in our points, we get $\left ( \frac{14}{2}, \frac{-4}{2}\right)$ .

So, our final answer is (7,-2) .

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Example Question #2 : How To Find The Midpoint Of A Line Segment

A line is drawn from (2,4) to (8,28). What are the coordinates of its midpoint?

Possible Answers:

$\left ( 5,20 \right )$

$\left ( 5,16 \right )$

$\left ( 3,12 \right )$

$\left ( 4,14 \right )$

Correct answer:

$\left ( 5,16 \right )$

Explanation:

The length to the midpoint is the difference between the two points divided by two. That number must then be added to the point:

$X_{midpoint}=X_{1}+\frac{\left (X_{2}-X_{1} \right )}{2}=2+\frac{\left (8-2 \right )}{2}=2+\frac{6}{2}=2+3=5$

$Y_{midpoint}=Y_{1}+\frac{\left (Y_{2}-Y_{1} \right )}{2}=4+\frac{\left (28-4 \right )}{2}=4+\frac{24}{2}=4+12=16$

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Example Question #7 : How To Find The Midpoint Of A Line Segment

A line segment begins at (2,3) and ends at the point (16,11) . What is the location of its midpoint?

Possible Answers:

(9,7)

(5,6)

(14,8)

(7,4)

(9,8)

Correct answer:

(9,7)

Explanation:

The difference in -values is 14 and the difference in -values is 8. The midpoint therefore differs by values of 7 and 4 from either of the endpoints.

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Example Question #3 : How To Find The Midpoint Of A Line Segment

$\textup{Two points }S\left ( 5,2\right )\textup{ and }T\left ( -3,10\right )\textup{ lie in the }xy\textup{-coordinate plane.}$

$\textup{What is the midpoint of line segment }\overline{ST}\textup{ ?}$

Possible Answers:

$\left ( 2,8\right )$

$\left ( 1,10\right )$

$\left (5,6\right )$

$\left ( 4,6\right )$

$\left ( 1,6\right )$

Correct answer:

$\left ( 1,6\right )$

Explanation:

$\textup{The coordinates of the midpoint are the averages of the other points' coordinates.}$

$x\textup{-coordinate}=\frac{5+\left ( -3)\right )}{2}=1\;\;\;\;y\textup{-coordinate}=\frac{2+10}{2}=6$

$\textup{The midpoint is at }\left (1,6\right )$

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Example Question #9 : How To Find The Midpoint Of A Line Segment

A line has endpoints of (5,-2) and (-1,0) . What is its midpoint?

Possible Answers:

(3,-1)

(1,1)

(2,1)

(2,-1)

(2,-2)

Correct answer:

(2,-1)

Explanation:

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

To find the midpoint of (5,-2) and (-1,0) , you simply plug in the points into the midpoint formula: $(\frac{5+-1}{2},\frac{-2+0}{2})$ , which gives you the point (2,-1) .

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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 #1 : Midpoint Formula

Example Question #2 : Midpoint Formula

Example Question #1 : How To Find The Midpoint Of A Line Segment

Example Question #32 : Coordinate Geometry

Example Question #3 : How To Find The Midpoint Of A Line Segment

Example Question #1 : How To Find The Midpoint Of A Line Segment

Example Question #2 : How To Find The Midpoint Of A Line Segment

Example Question #7 : How To Find The Midpoint Of A Line Segment

Example Question #3 : How To Find The Midpoint Of A Line Segment

Example Question #9 : How To Find The Midpoint Of A Line Segment

All Algebra 1 Resources

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