Method A:

To find the midpoint, draw the number line that contains points \(\displaystyle -7\) and \(\displaystyle 17\).  

Then calculate the distance between the two points.  In this case, the distance between \(\displaystyle -7\) and \(\displaystyle 17\) is \(\displaystyle 24\).  By dividing the distance between the two points by 2, you establish the distance from one point to the midpoint.  Since the midpoint is 12 away from either end, the midpoint is 5.

Method B:

To find the midpoint, use the midpoint formula:

\(\displaystyle M=\frac{x_{1}+x_{2}}{2}\)

\(\displaystyle M=\frac{-7+17}{2}\)

\(\displaystyle M=5\)

Translating the intersections into points on a graph, Janice works at (33,7) and Mark works at (15,5). The midpoint of these two points is found by taking the average of the x-coordinates and the average of the y-coordinates, giving ((33+15)/2 , (5+7)/2) or (24, 6). Traveling in one direction at a time, the number of blocks from either office to 24^th street is 9, and the number of blocks to 6^th is 1, for a total of 10 blocks.

On the number line,\(\displaystyle -7\) is \(\displaystyle 26\) units away from \(\displaystyle 19\).

\(\displaystyle 19-(-7)=26\)

We find the midpoint of this distance by dividing it by 2.

\(\displaystyle \frac{26}{2}=13\)

To find the midpoint, we add this value to the smaller number or subtract it from the larger number.

\(\displaystyle -7+13=6\ \text{or}\ 19-13=6\)

The midpoint value will be \(\displaystyle 6\).

Using the midpoint formula, \(\displaystyle m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\)

We get: \(\displaystyle (\frac{-4+3}{2},\frac{-6+7}{2})\)

Which becomes: which becomes \(\displaystyle (-\frac{1}{2},\frac{1}{2})\)

The midpoint of a line can be found using the midpoint formula, given by:

\(\displaystyle (x_{m},y_{m}) = \left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)\)

Thus when we plug in our values we get the midpoint is 

\(\displaystyle \left(\frac{3+-1}{2},\frac{2+8}{2} \right )\)

\(\displaystyle =\left(\frac{2}{2},\frac{10}{2} \right )\)

\(\displaystyle =(1,5)\)

To find the midpoint given two points, use the formula:

\(\displaystyle (\frac{x_1 +x_2}{2},\frac{y_1 +y_2}{2})\). Thus for our points we see:

\(\displaystyle (\frac{10+16}{2}, \frac{-18+8}{2})\) = \(\displaystyle (13,-5)\)

The midpoint can be found by using equations that calculate the values of its x- and y-coordinates. The x-coordinate can be found using the following equation:

\(\displaystyle \frac{x_{1} + x_{2}}{2}\) 

Likewise, we will calculate the y-coordinate using another formula:

\(\displaystyle \frac{y_{1} + y_{2}}{2}\) 

These formulas take the average of each coordinate separately in order to calculate the midpoint. In order to solve our question we will substitute in our given values and solve.

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

\(\displaystyle \left (\frac{1+7}{2},\frac{-4+8}{2} \right )=\left (\frac{8}{2},\frac{4}{2} \right )\)

\(\displaystyle \left (\frac{8}{2},\frac{4}{2} \right )=(4,2)\)

The midpoint formula must be used to find the midpoint of the line segment joining Jon's and Steve's houses. Use the following formula to find the midpoint:

\(\displaystyle \text{Midpoint}=\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)\)

In this formula, \(\displaystyle (x_{1},y_{1})\) and \(\displaystyle (x_{2}, y_{2})\) are the coordinates of the students' homes. Substitute in the coordinates of the houses and solve for the midpoint.

\(\displaystyle \text{Midpoint}=\left(\frac{(-3)+5}{2},\frac{4+8}{2}\right)\)

\(\displaystyle \text{Midpoint}=\left(1,6\right)\)

 In this case, the bus stop is at the following coordinate on the town map:

\(\displaystyle \left(1,6\right)\)

Putting the equation in y = mx + b form we obtain y = 1.5x – 2.5.

The slope is 1.5.

This question is asking us to find the x-intercept. Remember that the y-value is equal to zero at the x-intercept. Substitute zero in for the y-variable in the equation and solve for the x-variable.

\(\displaystyle \frac{1}{2}(0)+10=6x-2\)

\(\displaystyle 10=6x-2\)

Add 2 to both sides of the equation.

\(\displaystyle 10+2=6x-2+2\)

\(\displaystyle 12=6x\)

Divide both sides of the equation by 6.

\(\displaystyle \frac{12}{6}=\frac{6x}{6}\)

\(\displaystyle x=2\)

The line crosses the x-axis at 2.