1. 8-1 Midpoint and Distance Formulas

2. Midpoint Formula The midpoint of a
line segment with endpoints at (x1,y1) and (x2,y2) is the
point
Equal
distances
MIDPOINT

3. Find a midpoint of line segment…
With endpoints (-5,6) and (1,7)
Let (-5,6) = (x1,y1) and (1,7) = (x2,y2)
Midpoint formula
Substitute
Simplify

4. Find a midpoint of line segment…
With endpoints (4,5) and (14,13)
Let (4,5) = (x1,y1) and (14,13) = (x2,y2)
Midpoint formula
Substitute
Simplify

5. Distance Formula
The distance between two points with coordinates (x1,y1) and (x2,y2) is given by d=

6. Find the distance between…
points A(-3,6) and B(4,-4)
Let (-3,6) = (x1,y1) and (4,-4) = (x2,y2)
Distance formula
Substitute
Simplify

7. Find the distance between…
points A(2,-4) and B(10,-10)
Let (2,-4) = (x1,y1) and (10,-10) = (x2,y2)
Distance formula
Substitute
Simplify

8. Step it up… Midpoint formula Substitute and Write equations. and Solve
D(5,-1) is the midpoint of If C has coordinates (3,2),
what are the coordinates of E?
Midpoint formula
Substitute
and
Write equations.
and
Solve

9. Homework
P414: 11-19odd, 25-31odd, 35
Note: The answers are in the book. Your homework is to show, algebraically, that the answers are correct. If you get stuck, try (logon: BHSHAWKS06)
Simplify all radicals…DO NOT CONVERT TO DECIMAL FORM.