1. Distance & Midpoint in the Coordinate Plane

2. Coordinate Plane Ordered Pair: (x , y) A(2 , -1) Quad. II ( - , +)
y-axis (Dependent)
Quad. II
( - , +)
Quad. I
( + , +)
x-axis (Independent) A
Quad. III
( - , -)
Quad. IV
( + , -)

3. Graph the following equation.
y = 3x + 1
2 methods
x/y chart
Slope-Intercept Form
y-intercept
Slope

4. Graphing and finding the distance
Graph A(2 , -2) & B(2 , 6)
Graph C(1 , 2) & D(5 , 6)

5. Distance Formula dAB = √(x2 – x1)2 + (y2 – y1)2
Distance Formula: The distance (d) between two points
A(x1 , y1) and B(x2 , y2) is
dAB = √(x2 – x1)2 + (y2 – y1)2

6. Ex.1: Find the distance between the following points.
R(-2 , 6) & S(4 , 4)
x1 y1
x2 y2
dRS = √(x2 – x1)2 + (y2 – y1)2
= √(4 – (-2))2 + (4 – 6)2
= √(6)2 + (-2)2
= √36 + 4
= √40
= 6.3

7. To the nearest tenth, RS = 11.3.
Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth.
Let (x1, y1) be the point R(–2, –6) and (x2, y2) be the point S(6, –2).
d = (x2 – x1)2 + (y2 – y1)2 Use the Distance Formula.
d = (6 – (–2))2 + (–2 – (–6))2 Substitute.
d = (–8)2 Simplify.
d = =
Use a calculator.
To the nearest tenth, RS = 11.3.
1-6

8. Graphing the Midpoint Graph A(2 , -2) & B(2 , 6)
Graph C(1 , 2) & D(5 , 6)

9. ( ) M MidPoint Formula x2 + x1 y2 + y1 , 2 2
Midpoint Formula: The coordinates of the midpoint M of AB with endpoints A(x1 , y1) and B(x2 , y2) are the following: ( )
x2 + x1
y2 + y1 M , 2 2
y-coordinate of a point
x-coordinate of a point

10. ( ) ( ) ( ) M(1 , -3) Midpoint Example x2 + x1 y2 + y1 , M 2 2
AB has endpts A(8 , -9) & B(-6 , 3). Find the coordinates of its midpt. (
x2 + x1
y2 + y1 ) , M 2 2 (
(-6) + 8
3 + (-9) ) , M 2 2 ( ) 2 -6 , M 2 2
M(1 , -3)

11. y2 + y1 x2 + x1 2 2 y2 + 4 x2 +1 2 2 Midpoint Example G(-3 , 6) (2)
xm ym
G(-3 , 6)
The midpt of DG is M(-1 , 5).
One endpt is D(1 , 4).
Find the coordinates of the other endpts.
x1 y1
y2 + y1
x2 + x1
ym =
Xm = 2 2
y2 + 4
x2 +1
(2)
(2)
5 =
(2)
-1 =
(2) 2 2
10 = y2 + 4
-2 = x2 + 1
6 = y2
-3 = x2

12. ( ) M What have we learned??? dAB = √(x2 – x1)2 + (y2 – y1)2 x2 + x1
Distance Formula
Midpoint formula
dAB = √(x2 – x1)2 + (y2 – y1)2 ( )
x2 + x1
y2 + y1 M , 2 2
R(-2 , 6) & S(4 , 4)
x1 y1
x2 y2