1. Midpoints and Distance
Notes 1.6
Midpoints and Distance

2. Coordinate Plane X – axis – Horizontal Y-axis – Vertical
Points – represented by an ordered pair (x,y).

3. The Midpoint Formula
Used to find the midpoint of a segment on a graph.
Hint: Average the x’s and average the y’s.

4. Example 1: Finding the Coordinates of a Midpoint
Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).
= (–5, 5)

5. Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.
X M Y
(2, 7) (6, 1) (__, __)
Solution: (10, -5)

6. a2 + b2 = c2 To Find Distance Distance Formula Pythagorean Theorem
Too hard to use!!!!
Use Pythagorean Theorem instead
a2 + b2 = c2

7. Example 2: Finding Distance
Use the Pythagorean Theorem to find the distance, to the nearest tenth, from D(3, 4) to E(–2, –5).
a = 5 and b = 9.
c2 = a2 + b2 = =
= 106
c = 10.3