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High School Math : Algebra I

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Example Questions

Example Question #1 : Algebra I

What would be the midpoint of a line segment with endpoints at (0,1) $\displaystyle (0,1)$ and (5,7) $\displaystyle (5,7)$?

Possible Answers:

$(\frac{5}{2},\frac{9}{2})$ $\displaystyle (\frac{5}{2},\frac{9}{2})$

$(\frac{5}{2},4)$ $\displaystyle (\frac{5}{2},4)$

$(\frac{5}{2},\frac{5}{2})$ $\displaystyle (\frac{5}{2},\frac{5}{2})$

(5,6) $\displaystyle (5,6)$

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

Correct answer:

$(\frac{5}{2},4)$ $\displaystyle (\frac{5}{2},4)$

Explanation:

The midpoint of a line segment is halfway between the two $\small x$ $\displaystyle \small x$ values and halfway between the two $\small y$ $\displaystyle \small y$ values.

Mathematically, that would be the average of each coordinate: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ $\displaystyle (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$.

Plug in the (x,y) $\displaystyle (x,y)$ values from the given points and solve.

$(\frac{5+0}{2},\frac{7+1}{2})$ $\displaystyle (\frac{5+0}{2},\frac{7+1}{2})$

$(\frac{5}{2},\frac{8}{2})$ $\displaystyle (\frac{5}{2},\frac{8}{2})$

We can simplify the fraction to give our final answer.

$(\frac{5}{2},4)$ $\displaystyle (\frac{5}{2},4)$

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Example Question #1 : Midpoint And Distance Formulas

What would be the midpoint of a line segment with endpoints at (1,6) $\displaystyle (1,6)$ and (9,9) $\displaystyle (9,9)$?

Possible Answers:

$\displaystyle (2.5,7.5)$

$\displaystyle (4.5,4.5)$

(5,7.5) $\displaystyle (5,7.5)$

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

(0,0) $\displaystyle (0,0)$

Correct answer:

(5,7.5) $\displaystyle (5,7.5)$

Explanation:

The midpoint of a line segment is halfway between the two $\small x$ $\displaystyle \small x$ values and halfway between the two $\small y$ $\displaystyle \small y$ values.

Mathematically, that would be the average of each coordinate: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ $\displaystyle (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$.

Plug in the (x,y) $\displaystyle (x,y)$ values from the given points and solve.

$(\frac{9+1}{2},\frac{9+6}{2})$ $\displaystyle (\frac{9+1}{2},\frac{9+6}{2})$

$(\frac{10}{2},\frac{15}{2})$ $\displaystyle (\frac{10}{2},\frac{15}{2})$

Simplify the fractions to get the final answer.

(5,7.5) $\displaystyle (5,7.5)$

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

If a line has a midpoint at (2,5) $\displaystyle (2,5)$, and the endpoints are (0,0) $\displaystyle (0,0)$ and (4,y) $\displaystyle (4,y)$, what is the value of $\displaystyle y$?

Possible Answers:

$\displaystyle 4$

$\displaystyle 1$

2.5 $\displaystyle 2.5$

$\displaystyle 5$

$\displaystyle 10$

Correct answer:

$\displaystyle 10$

Explanation:

The midpoint of a line segment is halfway between the two $\small x$ $\displaystyle \small x$ values and halfway between the two $\small y$ $\displaystyle \small y$ values.

Mathematically, that would be the average of the coordinates: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ $\displaystyle (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$.

Plug in the (x,y) $\displaystyle (x,y)$ values from the given points.

$(\frac{4+0}{2},\frac{y+0}{2})=(2,5)$ $\displaystyle (\frac{4+0}{2},\frac{y+0}{2})=(2,5)$

Now we can solve for the missing value.

$(\frac{4}{2},\frac{y}{2})=(2,5)$ $\displaystyle (\frac{4}{2},\frac{y}{2})=(2,5)$

$\frac{4}{2}=2$ $\displaystyle \frac{4}{2}=2$

The $\small x$ $\displaystyle \small x$ values reduce, so both $\small x$ $\displaystyle \small x$ values equal $\small 2$ $\displaystyle \small 2$. Now we need to create a new equation to solve for the $\small y$ $\displaystyle \small y$ value.

$\frac{y}{2}=5$ $\displaystyle \frac{y}{2}=5$

Multiply both sides by $\displaystyle 2$ to solve.

$(2)\frac{y}{2}=5(2)$ $\displaystyle (2)\frac{y}{2}=5(2)$

y=10 $\displaystyle y=10$

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Example Question #3 : Algebra I

What is the midpoint of a line segment with endpoints (1,1) $\displaystyle (1,1)$ and (12,12) $\displaystyle (12,12)$?

Possible Answers:

$\displaystyle (11,-11)$

(13,13) $\displaystyle (13,13)$

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

$(\frac{13}{2},\frac{13}{2})$ $\displaystyle (\frac{13}{2},\frac{13}{2})$

(6,6) $\displaystyle (6,6)$

Correct answer:

$(\frac{13}{2},\frac{13}{2})$ $\displaystyle (\frac{13}{2},\frac{13}{2})$

Explanation:

The midpoint formula is this: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ $\displaystyle (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$.

Plug in the given values from our points and solve:

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

$(\frac{12+1}{2},\frac{12+1}{2})$ $\displaystyle (\frac{12+1}{2},\frac{12+1}{2})$

$(\frac{13}{2},\frac{13}{2})$ $\displaystyle (\frac{13}{2},\frac{13}{2})$

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Example Question #4 : Coordinate Geometry

What is the midpoint of the line segment with endpoints at (6,3) $\displaystyle (6,3)$ and (9,2) $\displaystyle (9,2)$?

Possible Answers:

$(\frac{9}{2},\frac{5}{2})$ $\displaystyle (\frac{9}{2},\frac{5}{2})$

$(\frac{2}{15},\frac{2}{5})$ $\displaystyle (\frac{2}{15},\frac{2}{5})$

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

$(\frac{2}{3},\frac{5}{3})$ $\displaystyle (\frac{2}{3},\frac{5}{3})$

$(\frac{15}{2},\frac{5}{2})$ $\displaystyle (\frac{15}{2},\frac{5}{2})$

Correct answer:

$(\frac{15}{2},\frac{5}{2})$ $\displaystyle (\frac{15}{2},\frac{5}{2})$

Explanation:

The midpoint formula is this: $(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$ $\displaystyle (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$.

Plug in the given values from our points and solve:

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

$(\frac{9+6}{2},\frac{2+3}{2})$ $\displaystyle (\frac{9+6}{2},\frac{2+3}{2})$

$(\frac{15}{2},\frac{5}{2})$ $\displaystyle (\frac{15}{2},\frac{5}{2})$

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

Find the midpoint between (4, 3) and (6, 9).

Possible Answers:

$\left ( 0,6 \right )$ $\displaystyle \left ( 0,6 \right )$

$\left ( -5,6 \right )$ $\displaystyle \left ( -5,6 \right )$

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

$\left ( 5,6 \right )$ $\displaystyle \left ( 5,6 \right )$

$\left ( 6,5 \right )$ $\displaystyle \left ( 6,5 \right )$

Correct answer:

$\left ( 5,6 \right )$ $\displaystyle \left ( 5,6 \right )$

Explanation:

Add up the $\displaystyle x$'s and divide in half, which results in 5. Do the same to the $\displaystyle y$'s and you get 6. Put the $\displaystyle x$ and $\displaystyle y$ in an ordered pair so that your answer is (5, 6).

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Example Question #4 : Algebra I

What is the midpoint of the line segment which connects (-6, 8) $\displaystyle (-6, 8)$ and (2, 12) $\displaystyle (2, 12)$?

Possible Answers:

$\displaystyle (-4, 20)$

$\displaystyle (-8, -4)$

(8, 4) $\displaystyle (8, 4)$

$\displaystyle (-2, 10)$

(2, 10) $\displaystyle (2, 10)$

Correct answer:

$\displaystyle (-2, 10)$

Explanation:

To find the midpoint of a line segment, we find the average of the x and y coordinates of the endpoints. The average of two numbers is the sum of those numbers divided by $\displaystyle 2$. Thus, to find the x-coordinate of our midpoint, we find the average of $\displaystyle -6$ and $\displaystyle 2$, and we get $\displaystyle (-6+2)/2=-4/2 = -2$.

To find the y-coordinate of our midpoint, we find the average of $\displaystyle 8$ and $\displaystyle 12$, which is $\displaystyle (8+12)/2=20/2 = 10$.

Thus, our midpoint is $\displaystyle (-2, 10).$

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Example Question #6 : Coordinate Geometry

Find the midpoint of the line segment with end points (-2,3) $\displaystyle (-2,3)$ and (-4,16) $\displaystyle (-4,16)$.

Possible Answers:

(6,-19) $\displaystyle (6,-19)$

(-6,19) $\displaystyle (-6,19)$

(3,9.5) $\displaystyle (3,9.5)$

$\displaystyle (3,-9.5)$

$\displaystyle (-3,9.5)$

Correct answer:

$\displaystyle (-3,9.5)$

Explanation:

To find the midpoint of a line segment, use the standard equation:

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

Plugging in the given points:

$(\frac{-2+-4}{2},\frac{3+16}{2})=(-3,9.5)$ $\displaystyle (\frac{-2+-4}{2},\frac{3+16}{2})=(-3,9.5)$

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Example Question #7 : Coordinate Geometry

Find the midpoint of these two points:

(-2,13) $\displaystyle (-2,13)$ and (4,-9) $\displaystyle (4,-9)$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

The standard formula to find the midpoint of two points is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ $\displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

Plug in the given points to find the answer:

$(\frac{-2+4}{2},\frac{13+(-9)}{2})=(\frac{2}{2},\frac{4}{2})=(1,2)$ $\displaystyle (\frac{-2+4}{2},\frac{13+(-9)}{2})=(\frac{2}{2},\frac{4}{2})=(1,2)$

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Example Question #2 : Algebra I

A line segment has endpoints at (2,3) $\displaystyle (2,3)$ and (-7,3) $\displaystyle (-7,3)$. What is the midpoint of this segment?

Possible Answers:

$\displaystyle (-4.5,0)$

(9,3) $\displaystyle (9,3)$

(-5,3) $\displaystyle (-5,3)$

$\displaystyle (-2.5,3)$

$\displaystyle (-4.5,3)$

Correct answer:

$\displaystyle (-2.5,3)$

Explanation:

My midpoint will be at the average of the $\displaystyle x$-values and the average of the $\displaystyle y$-values. Mathematically, $(\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})$ $\displaystyle (\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})$.

Plug in our given values.

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

$(\frac{-7+2}{2}, \frac{3+3}{2})$ $\displaystyle (\frac{-7+2}{2}, \frac{3+3}{2})$

$(\frac{-5}{2}, \frac{6}{2})$ $\displaystyle (\frac{-5}{2}, \frac{6}{2})$

$\displaystyle (-2.5,3)$

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High School Math : Algebra I

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Algebra I

Example Question #1 : Midpoint And Distance Formulas

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

Example Question #3 : Algebra I

Example Question #4 : Coordinate Geometry

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

Example Question #4 : Algebra I

Example Question #6 : Coordinate Geometry

Example Question #7 : Coordinate Geometry

Example Question #2 : Algebra I

All High School Math Resources

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