1. 9.1 Distance Formula & Midpoint Formula

2. Distance Find the distance between the 2 points What theorem ?
(3, 4) 4
What theorem ?
Pythagorean
(0, 0) 3 c b a
Why not ± ?
Distance
Distance Formula:

3. Ex 1) Find the distance between (2, –1) and (9, 1)
(x1, y1)
(x2, y2)

4. T.O.O Ex 2) Find the distance between
(x1, y1)
(x2, y2)

5. Ex 3) Find the distance between (a, b) and (0, b)
(x1, y1)
(x2, y2)

6. Midpoint Formula What does midpoint mean? Middle Midpoint Formula:
(3, 4)
approx
What does midpoint mean?
Middle
(0, 0)
Midpoint Formula:
Add them up & divide by 2
Midpoint is +
Distance is –

7. Ex 4) Find the midpoint of (6, 4) and (2, 8)
Midpoint Formula:

8. Ex 5) If the midpoint is (–1, 1) and one endpoint is (–6, 2), find the other endpoint.
(x1, y1) = (–6, 2)
Find (x2, y2)
Set each part = to each other

9. Ex 6) Find the equation in Standard Form of the perpendicular bisector of AB for the points A(–2, 1) and B(1, –3).
Perp. Bisector: Opp. recip. slope & goes through midpoint.
Find the slope of the line.
Find the opp. recip. slope.
Find the midpoint of the 2 points
Perp. Bis. has slope and goes thru point

10. Slope: Point: S.F.: No Fractions Ax + By = C A is (+)
Use slope formula again:
S.F.: No Fractions
Ax + By = C
A is (+)
(2)
(2)
(2)
(2)

11. T.O.O. Ex 7) Find the midpoint and distance of (–a, b) and (2a, 4b)
Midpoint Formula:
Distance Formula:

12. Homework
#901 Pg – 23 odd Pg – 4 all