To get from the midpoint of (12, –3) to point (3,4), we travel –9 units in the x-direction and 7 units in the y-direction. To find the other point, we travel the same magnitude in the opposite direction from the midpoint, 9 units in the x-direction and –7 units in the y-direction to point (21, –10). 

The midpoint formula can be used to solve this problem, where the midpoint is the average of the two coordinates.

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

We are given the midpoint and one endpoint. Plug these values into the formula.

\(\displaystyle (4,-1)=(\frac{-4+x}{2},\frac{3+y}{2})\)

\(\displaystyle 4=\frac{-4+x}{2}\ \text{and}\ -1=\frac{3+y}{2}\)

Solve for the variables to find the coordinates of the second endpoint.

\(\displaystyle 8=-4+x\ \text{and}\ -2=3+y\)

\(\displaystyle 12=x\ \text{and}\ -5=y\)

The final coordinates of the other endpoint are \(\displaystyle (12,-5)\).

The midpoint of a line segment is found using the formula \(\displaystyle \left ( \frac{x_1+x_2 }{2}, \frac{y_1+y_2}{2}\right )\).

The midpoint is given as \(\displaystyle (4,12).\) Going through the answer choices, only the points \(\displaystyle (2,8)\) and \(\displaystyle (6,16)\) yield the correct midpoint of \(\displaystyle (4,12)\).

 \(\displaystyle \left ( \frac{2+6}{2}, \frac{8+16}{2} \right )=(4,12)\)

What is the midpoint of the segment of 

\(\displaystyle 2y = 3x + 22\)

between \(\displaystyle x = 4\) and \(\displaystyle x = 10\)?

To find this midpoint, you must first calculate the two end points.  Thus, substitute in for \(\displaystyle x\):

\(\displaystyle 2y = 3* 4+22\)

\(\displaystyle 2y = 34\)

\(\displaystyle y=17\)

Then, for \(\displaystyle x = 10\):

\(\displaystyle 2y = 3 * 10 +22\)

\(\displaystyle 2y = 52\)

\(\displaystyle y=26\)

Thus, the two points in question are:

\(\displaystyle (4,17)\) and \(\displaystyle (10,26)\)

The midpoint of two points is:

\(\displaystyle (\frac{x_1+x_0}{2},\frac{y_1+y_0}{2})\)

Thus, for our data, this is:

\(\displaystyle (\frac{4+10}{2},\frac{17+26}{2})\)

or

\(\displaystyle (7,21.5)\)

Recall that the midpoint's \(\displaystyle x\) and \(\displaystyle y\) values are the average of the \(\displaystyle x\) and \(\displaystyle y\) values of the two points in question.   Thus, if we call the other point \(\displaystyle (x,y)\), we know that:

\(\displaystyle -10 = \frac{-20+x}{2}\) and \(\displaystyle -3 = \frac{15+y}{2}\)

Solve each equation accordingly:

For \(\displaystyle -10 = \frac{-20+x}{2}\), multiply both sides by \(\displaystyle 2\):

\(\displaystyle -20=-20+x\)

Thus, \(\displaystyle x=0\)

The same goes for the other equation:

\(\displaystyle -6=15+y\), so \(\displaystyle y=-21\)

Thus, our point is \(\displaystyle (0,-21)\) 

If \(\displaystyle (15,40)\) is the midpoint of \(\displaystyle (5,10)\) and another point, what is that other point?

Recall that the midpoint's \(\displaystyle x\) and \(\displaystyle y\) values are the average of the \(\displaystyle x\) and \(\displaystyle y\) values of the two points in question. Thus, if we call the other point \(\displaystyle (x,y)\), we know that:

 \(\displaystyle 15 = \frac{5+x}{2}\)and \(\displaystyle 40 = \frac{10+y}{2}\)

Solve each equation accordingly:

For \(\displaystyle 15 = \frac{5+x}{2}\), multiply both sides by \(\displaystyle 2\) and then subtract \(\displaystyle 5\) from both sides:

\(\displaystyle 30=5+x\)

Thus, \(\displaystyle x=25\)

For \(\displaystyle 40 = \frac{10+y}{2}\), multiply both sides by 2 and then subtract 10 from both sides: 

Thus, \(\displaystyle y=70\)

Thus, our point is \(\displaystyle (25,70)\)

The midpoint formula is 

The midpoint formula is equal to . Add the x-values together and divide them by 2, and do the same for the y-values.

x: (2 + 8) / 2 = 10 / 2 = 5

y: (6 + 4) / 2 = 10 / 2 = 5

The midpoint of MN is (5,5).

The midpoint formula is  . An easy way to remember this is that finding the midpoint simply requires that you find the averageof the two x-coordinates and the average of the two y-coordinates. In this case, the two x-coordinates are 3 and 7, and the two y-coordinates are 5 and 9. If we substitute these values into the midpoint formula, we get (3 + 7/2), (5 + 9)/2, which equals (5, 7). If you got (–2, –2), you may have subtracted your x and y-coordinates instead of adding. If you got (10,14), you may have forgotten to divide your x and y-coordinates by 2. If you got (6,6), you may have found the average of x_{1 and} y₂ and x₂ and y₁ instead of keeping the x-coordinates together and the y-coordinates together. If you got (7, 5), you may have switched the x and y-coordinates.

The formula for midpoint = (x₁ + x₂)/2, (y₁ + y₂)/2. Substituting in the two x coordinates and two y coordinates from the endpoints, we get (–1 + 3)/2.

(4 + 6)/2 or (1, 5) as the midpoint.