/Geo_Sec._1.3

Chapter 1 - Essentials of Geometry Section 1.3 - Use Midpoint and Distance formulas What the student should get from this: 1. Develop and apply the formula for midpoint 2. Use the distance formula and the Pythagorean Theorem to find the distance between two points Let始s start with the midpoint of a segment... that is a location, not a length.

Locate the midpoint of AB .

y

B.

A.

x

Example: Find the midpoints of the following segments: A(2, 5), B(-2, 10), C(4, 5), D(12, 3) "AB

"

"

"

"

"

DB

"BC

"

"

"

"

"

CD

Example: Given point F(14, -6), what are the coordinates of point D if point M(3, 8) is the midpoint of DF ?

Examples: M is the midpoint of segment DE. Find the coordinates for E given the following information: D(9, 6), M(18, 2)

D(-7, 14), M(28, 6)

Now for the Pythagorean Theorem in the coordinate plane... a + b = c 2

2

2

c

a b

You can also use the distance formula which is a derivative of the Pythagorean Theorem...

d = (x2 − x1 )2 + (y2 − y1 )2 for any two points (x1 , y1 ) and (x2 , y2 ) Example: Given points A(2, 5), B(8, -2), C(6, 12), find: AB =

AC =

BC = " " " " " " Assignment: p.19 #s 2-16 even, 17, 19, 20, 23, 25, 26, 31-33 all, 42, 47. Show work.

Draw all pictures.