9.1 Distance Formula & Midpoint Formula

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Presentation transcript:

9.1 Distance Formula & Midpoint Formula

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:

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

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

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

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 –

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

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

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

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)

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

Homework #901 Pg. 404 1 – 23 odd Pg. 405 1 – 4 all