POINT
TOPIC 10: COORDINATES OF A POINTS ~ MATHEMATICS FORM 1
The plane used is called 𝑥𝑦 − plane and it has two axis; horizontal axis known as 𝑥 − axis and; vertical axis known as 𝑦 − axis
The x-coordinate (alwayscomes first.
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The first number (the first coordinate) isalwayson the horizontal axis.
A Point on the Coordinates
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To locate (2,5), move 2 units to the right on thex-axis and 5 units up on they-axis.
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The order in which you writex– andy-coordinates in an ordered pair is very important.
Gradient or slope of a line – is defined as the measure of steepness of the line.
change in 𝑥.
Consider two points 𝐴 (𝑥1, 𝑦1)and (𝐵 𝑥2, 𝑦2), the slope between the two points is given by:
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Example 1
- (5, 1) and (2,−2)
- (4,−2) and (−1, 0)
- (−2,−3) and (−4,−7)
Example 2
- The line joining (2,−3) and (𝑘, 5) has gradient −2. Find 𝑘
- Find the value of 𝑚 if the line joining the points (−5,−3) and (6,𝑚) has a slope of½
The gradient and the 𝑦 − intercept (at x = 0) or 𝑥 − intercept ( at y=0)
The gradient and a point on the line
Since only one point is given, then
Two points on the line
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Example 3
Gradient 2 and 𝑦 − intercept −4
Gradient −2⁄3and passing through the point (2, 4)
Passing through the points (3, 4) and (4, 5)
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The equation of a line can be expressed in two forms
- 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0 and
- 𝑦 = 𝑚𝑥 + 𝑐
- 2𝑦 = 5𝑥 + 1
- 2𝑥 + 3𝑦 = 5
- 𝑥 + 𝑦 = 3
Intercepts
- to get 𝑥 − intercept, let 𝑦 = 0 and
- to get 𝑦 − intercept, let 𝑥 = 0
Example 5
- By using intercepts
- By using the table of values
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Example 6
The Graph of a Linear Equation
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equations.
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Example 7
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