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## Coordinate Geometry

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### Coordinate Geometry The Cartesian Plane and Gradient ... – PowerPoint PPT presentation

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Title: Coordinate Geometry

1
Coordinate Geometry
• The Cartesian Plane and Gradient

2
Basic Terminology
• The figure on the right shows 2 perpendicular
lines intersecting at the point O. This is called
the Cartesian Plane.
• O is also called the origin.
• The horizontal line is called the x-axis and the
vertical line is called the y-axis

3
Coordinates of a Point
• The position of any point in the Cartesian Plane
can be determined by its distance from each axes.
• Example Point A is 3 units to the right of the
y-axis and 1 unit above the x-axis, its position
is described by the coordinate (3, 1).
• Similarly, the coordinates of Points B, C and D
are determined as shown.

4
Question
• What coordinate represents the origin O ?
• Ans (0, 0)

5
Summary
• Any point, P, in the plane can be located by its
coordinate (x, y).
• We call x the x - coordinate of P and y the
y - coordinate of P.
• Hence, we say that P has coordinates (x, y).

6
Solution to Exercise 1
7
• The steepness of a line is called its GRADIENT
(or slope).
• The gradient of a line is defined as the ratio of
its vertical distance to its horizontal distance.

8
What is the gradient of the driveway?
Ans
9
An assembly line is pictured below. What is the
Ans
10
The bottom of the playground slide is 2.5 m from
which represents the slide is 0.68. How tall is
the slide?
Ans
11
Question
• For safety considerations, wheelchair ramps are
constructed under regulated specifications. One
regulation requires that the maximum gradient of
a ramp exceeding 1200 mm in length is to be
• (a) Does a ramp 25 cm high with a horizontal
length of 210 cm meet the requirements?
• (b) Does a ramp with gradient meet the
specifications?
• (c) A 16 cm high ramp needs to be built. Find
the minimum horizontal length of the ramp
required to meet the specifications.

Ans No
Ans Yes
Ans 224 cm
12
Horizontal and Vertical Lines
• The gradient of a horizontal line is ZERO
• (Horizontal line is flat No Slope)
• The gradient of a vertical line is INIFINITY
• (Vertical line gradient is maximum)

13
Finding the gradient of a straight line in a
Cartesian Plane
• Lines that climb from left to the right are said
• Lines that descend from left to the right are

14
Examples
Write down the coordinates of the points given
(16, 0)
(0, 10)
(0, -8)
(-15, 0)
15
Examples
(-4, 0)
(0, 6)
(3, 0)
(0, -12)
16
Summary
Infinite
17
• So far, we have determined the gradient using the
• idea of
• Using the above, we must always remember to add a
negative sign to slopes with negative gradient.
• Now, lets look at the formula to determine
gradient. The formula will take into
consideration the sign of the slope

18
19
• Write down the coordinates of 2 points on the
line (x1, y1) and (x2, y2)
• If the coordinate is negative, include its sign
• Apply the formula

20
Examples
(1, 4)
L1 2 points on the line are (1, 4) and (0, 1)
(0, 1)
Tip Choose points that are easy to read!
1 square represents 1 unit on both axes
21
Examples
L2 2 points on the line are (1, 1) and (3, 3)
Tip Choose points that are easy to read!
1 square represents 1 unit on both axes
22
Examples
L3 2 points on the line are (3, 1) and (1, 0)
1 square represents 1 unit on both axes
23
Examples
L4 2 points on the line are (3, -1) and (-3,
-3)
1 square represents 1 unit on both axes
24
Examples
L5 2 points on the line are (0, 1) and (1, -2)
1 square represents 1 unit on both axes
25
Examples
L6 2 points on the line are (0, 0) and (-4, 4)
1 square represents 1 unit on both axes
26
Examples
L7 2 points on the line are (4, -2) and (-2, 2)
1 square represents 1 unit on both axes
27
Examples
L8 2 points on the line are (0, -2) and (-3,
-1)
1 square represents 1 unit on both axes
28
Question
• Is there a difference between

Ans No.
• Is there a difference between

Ans Yes!
29
Solution to Exercise 2
In order from smallest to largest gradient e, b,
a, d, c
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3
Horizontal Line Zero Vertical Line Inifinity