Distance and Midpoint Formulas Red Book Lesson 4.1

EQ: How do you find the distance between two points EQ: How do you find the distance between two points? How do you find the midpoint of a segment?

Vocabulary The Distance Formula The distance d between any two points (x1, y1) and (x2, y2) is d = √(x2 – x1)2 + (y2 – y1)2

Example 1 What is the distance between the points (3, 4) and (0, 0)? First, label your original points: x1 = 3, y1 = 4, x2 = 0, y2 = 0 Next, Plug and Chug: d = √(0 – 3)2 + (0 – 4)2 = √ 9 + 16 = √25 So the distance between the points is d = 5

The point equidistant from the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two congruent segments (equal parts).

x-coordinates and the average (mean) of the y-coordinates. The Midpoint Formula: The midpoint of a segment with endpoints (x1 , y1) and (x2 , y2) has coordinates When you are finding the coordinates of the midpoint of a segment, you are actually finding the average (mean) of the x-coordinates and the average (mean) of the y-coordinates. The Midpoint Formula works for all line segments:  vertical, horizontal or diagonal.

Example 2 Find the midpoint of the segment with endpoints (3, 4) and (0, 0). First, label your original coordinates: x1 = 3, y1 = 4, x2 = 0, y2 = 0 Next, Plug and Chug: ((3+0)/2, (4 + 0)/2) So the coordinates of the midpoint are (3/2, 2)