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Distance on the Coordinate Plane

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by

Susan Bryan

on 23 October 2013

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Transcript of Distance on the Coordinate Plane

Graphing Ordered Pairs
Graph A (-5,7).
Start at the origin and go left 5 squares on the x-axis.
Go up 7 squares.
Draw a dot and label it A (-5,7).
What is an Ordered Pair?
A point on a coordinate plane has a value on the x-axis and a value on the y-axis.
Together those values are an "
ordered pair
".
We sometimes call them the
coordinates
of a point.



The coordinates are always written (x,y).


Distance on the Coordinate Plane
We can use what we know about the coordinate plane and the Pythagorean Theorem to calculate the distance between points.
If A(-4,-2) and B(2,6), we can draw a right triangle. Counting the squares, the x distance is 6 and the y distance is 8.
Using the Pythagorean Theorem, the distance d between A and B is 10.
6 + 8 = d
36 + 64 = 100
d = 10
Distance on the Coordinate Plane
x-axis
: the horizontal
number line
What is a Coordinate Plane?
Origin
: where the two number lines intersect


y-axis

: the vertical number line
Quadrants
: the four sections of the coordinate plane
Q IV
Q I
Q II
Q III
abscissa: x-axis value
ordinate: y-axis value
This point is at (3,5). That is, the x-coordinate is 3. The y-coordinate is 5.
(3,5)
We could also say the abscissa is 3 and the ordinate is 5.
P
Number Lines
Number Lines don't have to be from side to side.
They can be up an down, from top to bottom. If we rotate it 90 degrees, it looks like this.
We will call the numbers on the side to side line "x" and the up and down line "y"
x
y
Naming an Ordered Pair
Start at the origin
Move right to find the x-coordinate (4)
Move up to find the y-coordinage (2)

The coordinates of point P are (4,2)
Point B has coordinates of (-2, -3). We would write this as B (-2,-3).

What are the coordinates of these points?
C ( , )
D ( , )
E ( , )
B
C
D
E
A (-5,7)
Your Job
Using a piece of graph paper, draw a coordinate plane.
Label the origin, x- and y-axis, and which directions are positive and which directions are negative.

Plot the following points on your graph:
M(-2,6) N(-4,-5)

O(3,-4) P(7,5)


}
}
A(-4,-2)
B(2,6)
6
8
d
2
2
2
2
Graph the followning pairs of coordinates.
Find the distance between the points. Round to three places.

A. (2,0), (5,-4) B. (1,3),(-2,4) C. (-3,-4),(2,-1)
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