Answer:
If you are given two numbers, you can find the number exactly between them by averaging them, by adding them together and dividing by two. For example, the number exactly halfway between 5 and 10 is:
{5 + 10}{2} = {15}{2} = 7.5
2 5+10 = 215 =7.5
Find the midpoint P between (–1, 2) and (3, –6).
First, I apply the Midpoint Formula; then, I'll simplify:
({-1 + 3}{2},{2 + (-6)}{2})( 2−1+3, 22+(−6)) = ({2}{2},{-4}{2}) = (1,,-2)=( 22 , 2−4 )=(1,−2)
So the answer is P = (1, –2).
The midpoint of two points, (x1, y1) and (x2, y2) is the point M
M =({x_1 + x_2}{2},{y_1 + y_2}{2})M=( 2 x 1+x 2, 2 y 1+y 2)
But as long as you remember that you're averaging the two points' x- and y-values, you'll do fine. It won't matter which point you pick to be the "first" point you plug in. Just make sure that you're adding an x to an x, and a y to a y.
Find the midpoint P between (6.4, 3) and (–10.7, 4).
{6.4 + (-10.7)}{2}{3 + 4}{2})( 2
6.4+(−10.7) , 2 3+4 )
= {-4.3}{2},{7}{2}) = (-2.15,\,3.5)=( 2−4.3 , 2 7 )=(−2.15,3.5)
So the answer is P = (–2.15, 3.5).
Find the value of p so that (–2, 2.5) is the midpoint between (p, 2) and (–1, 3).
{p + (-1)}{2},{2 + 3}{2}) = (-2,\2.5)( 2p+(−1) , 2 2+3 )=(−2,2.5)
{p - 1}{2},{5}{2}) = (-2,,2.5)( 2 p−1 , 2 5 )=(−2,2.5)
(p - 1}{2},\,2.5) = (-2,,2.5)(2p−1,2.5)=(−2,2.5)
The y-coordinates already match. This reduces the problem to needing to compare the x-coordinates, "equating" them (that is, setting them equal, because they must be the same) and solving the resulting equation to figure out what p is. This will give me the value necessary for making the x-values match. So:
p - 1}{2} = -2
2p−1 =−2
p - 1 = -4p−1=−4
p = -3p=−3
So the answer is p = –3.
Explanation: