Scale X-axis Y-axis

Scales for the coordinate Axis.

Learning outcomes :

1.  Mark the values on both axis by extending the sequence of given values on the axis.

2.  State the scales used in given coordinate axis where:

                               I.            Scale for the axis are the same.

                              II.           Scale for the axis are difference.

3.  Mark the values on both axis, with reference to the scales given.

4. state the coordinate of a given point, with reference to the scales given.

5. plot point , given the coordinate, with reference scales given.

6. pose and solve problem involving the coordinate.

                         Scale for the coordinate axes refer to the ratio which shows the values on the axes that is represented by one units.

Scales Used on the Coordinate Axes

1 unit on the x-axis represents 2 units.

1 unit on the y-axis represents 2 units.

Therefore, the scale for x and y-axis is 1 :  2.

1 unit on the x-axis represents 5 units.

1 unit on the y-axis represents 3 units.

Therefore, the scale for the x-axis is 1 : 5 and the scale for the y-axis is 1 : 3.

Example :

State the coordinates of point P and point Q in each of the Cartesian plane shown below.

a)

        

solution:

The coordinates of P are (-9,40)  --> P is 9 units to the left of the y-axis, 40 units above the x-axis.
The coordinates of Q are (6,40)  --> Q is 6 units to the right of the y-axis, 40 the x-axis.

b)

solution
The coordinates of P are (15,8)  --> P is 15 units to the right of the y-axis, 8 units above the x-axis.
The coordinates of Q are (-10, -8)  --> Q is 10 units to the left of the y-axis, 8 units below the  x-axis.

Values on the x-axis and y-axis Based on Given Scales for Both Axes

 Example:

Mark the values on the x-axis and the y-axis on a Cartesian plane if the scale for the x-axis is 1 : 3 and 

the scale for the y-axis is 1 : 5.

*the scale for the x-axis is 1:3

 this is show 1 units represents for 3 units

*the scale for the y-axis is 1:5

this is show 1 units represents for 5 units.

solution

Stating the Coordinates of a Point Based on Given Scales for Both Axes

Example:

State the coordinates of each point marked on the Cartesian plane.

P(-5, 20)

Q(0, 14)

R(8, - 10)

S(-7, -12)

Plotting Points with Given Coordinates Based on Given Scales

Example:

Plot points A(1, 5) and B(-2, 20) on a Cartesian plane if the scale for the x-axis is 1 : 1 and the 

scale for the y-axis is 1 : 5.