1. Midpoint and distance formulas 9-1-15
Geometry Ch 1-7
Midpoint and distance formulas
9-1-15

2. Try these (You don’t have to write your answer, but be ready to explain out loud if you don’t)

3. Pythagorean theorem
We can use what we know about the Pythagorean theorem to find distance and midpoint between two coordinates on the coordinate plane.
The dotted lines are the legs of a right triangle, we can easily find those lengths and use them to determine the hypotenuse.
Notice that the dotted lines are just the difference between the two x values or the two y values.

4. Distance formula This means that D2=A2+B2 Is the same as
The Horizontal distance between the two points = a in the Pythagorean theorem.
The vertical distance between the two points =b in the Pythagorean theorem.
So,
Y2-Y1= B
X2-X1= A
This means that
D2=A2+B2
Is the same as
D= X2−X1 2+ (Y2−Y1) 2 D A B

5. Memorize this… D= X2−X1 2+ (Y2−Y1) 2
The legs of a right triangle are the difference between x values or y values
Square the differences
Add the squares
Find the square root of the sum
OR This…
D= X2−X1 2+ (Y2−Y1) 2

6. Midpoint Formula
Similarly, we can find the midpoint of d by finding the halfway point of a and b.
Because the distance NM is really just the difference in x values and LN is just the difference in y values, we can find their averages to find the midpoint of LM
The formula for this is:
X2+X1 2 , Y2+Y1 2
Subscripts don’t matter, just keep them in order…2,1;2,1 or 1,2;1,2 L d a M N b

7. Remember
The midpoint formula uses + signs because we are finding a coordinate, the distance formula uses – signs because we are finding an actual distance.
Your best move is always to label your coordinates with
Y2 Y1 and X2 X1