Download 1-6 The Coordinate Plane

1-6 THE COORDINATE PLANE (p. 43-49)
In the coordinate plane, a point is described by an ordered pair of numbers called the
x and y coordinates of the point.
Example: Sketch the coordinate plane and review the four quadrants, the two axes, and
the origin. In what quadrants are the x-coordinates positive? negative? In what
quadrants are the y-coordinates positive? negative?
If two points are on a horizontal or vertical line, you can find the distance between them
by using the Ruler Postulate (use absolute value and subtraction).
Example: Find the distance between two points that lie on a horizontal line that goes
through -4 on the y axis.
Example: Find the distance between two points that lie on a vertical line that goes
through 6 on the x axis.
If two points do not lie on either a horizontal or vertical line (that is, they lie on a
diagonal or slanted line), you can not use simple subtraction to find the distance between
them. You must use the Distance Formula to find the distance between these two points.
The Distance Formula
The distance d between two points A (x1 , y1 ) and B (x 2 , y 2 ) is
d  (x 2  x 1 ) 2  ( y 2  y1 ) 2 .
Example: Find the distance between C (-2,6) and D (6,-2) to the nearest tenth. This will
give an approximate answer. Also briefly discuss simplest radical form which will give
an exact answer.
Do 1 a and b on p. 44.
Do 2b on p. 44.
To find the coordinate of the midpoint of a segment on a number line, simply find the
average or arithmetic mean of the coordinates of the two endpoints.
Example:
J
K
-6
13
J and K lie on a number line. Find the coordinate of the midpoint of JK.
When you find the coordinates of the midpoint of a segment in the coordinate plane, you
use the averaging process twice- once for the x-coordinates and once for the ycoordinates.
The Midpoint Formula
The coordinates of the midpoint M of AB with endpoints
A (x1 , y1 ) and B (x 2 , y 2 ) are the following:
x  x 2 y1  y 2
M( 1
,
)
2
2
Example: AB has endpoints (8,9) and (-3,-15). Find the coordinates of the midpoint M.
Sometimes you may know the coordinates of the midpoint and one endpoint, and you
need to find the coordinates of the second endpoint. You still use the midpoint formula
to find the coordinates of the other endpoint, but in a slightly different fashion.
Example: The midpoint of DG is M (-1,5). One endpoint is D (1,4). Find the
coordinates of the other endpoint G.
If time, do 4 on p. 45.
Have students copy my Distance and/or Midpoint Formula programs from my TI
program collection.
Homework p. 46-49: 5,7,15,20,23,27,29,41,50,64,65,74,76,78
50. Use the distance formula program to get an answer in grid units. Multiply this answer
by 0.1 to convert to miles.