Sec. 1 8 The Coordinate Plane

1
Sec. 1 8 The Coordinate Plane

• Objectives
• 1) Find the distance between 2 points on the
  coordinate plane.
• 2) Find the coordinate of the midpoint of a
  segment on the coordinate plane.

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

• Distance Formula The distance (d) between two
  points
• A(x1 , y1) and B(x2 , y2) is

dAB v(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 v(x2 x1)2 (y2 y1)2
v(4 (-2))2 (4 6)2
v(6)2 (-2)2
v36 4
v40
6.3
7

Let (x1, y1) be the point R(2, 6) and (x2, y2)
be the point S(6, 2).
d 82 (8)2 Simplify.
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
MidPoint formula

• 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
Ex.2
x1 y1
x2 y2

• 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
Ex.3
xm ym

• The midpt of DG is M(-1 , 5).
• One endpt is D(1 , 4).
• Find the coordinates of the other endpts.

G(-3 , 6)
x1 y1
y2 y1
x2 x1
ym
Xm
2
2
y2 4
x2 1
(2)
(2)
5
-1
(2)
(2)
2
2
10 y2 4
-2 x2 1
6 y2
-3 x2
12
What have we learned???

• Distance Formula
• Midpoint formula

dAB v(x2 x1)2 (y2 y1)2
(
)
x2 x1
y2 y1
M
,
2
2

• R(-2 , 6) S(4 , 4)

x1 y1
x2 y2