**POINT**

**TOPIC 10: COORDINATES OF A POINTS ~ MATHEMATICS FORM 1**

**Coordinates of a points**– are the values of 𝑥 and 𝑦 enclosed by the bracket which are used to describe the position of a point in the plane

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 (*always*comes first.

**COORDINATES OF A POINTS**

The first number (the first coordinate) is*always*on the horizontal axis.

A Point on the Coordinates

*x*-coordinate is 2.

*y*-coordinate is 5.

**COORDINATES OF A POINTS**

To locate (2,5), move 2 units to the right on the*x*-axis and 5 units up on the*y*-axis.

**COORDINATES OF A POINTS**

The order in which you write*x*– and*y*-coordinates in an ordered pair is very important.

*x*-coordinate always comes first, followed by the

*y*-coordinate.

**Gradient (Slope) of a Line**

Gradient or slope of a line – is defined as the measure of steepness of the line.

change in 𝑥.

Consider two points 𝐴 (𝑥_{1}, 𝑦_{1)}and (𝐵 𝑥_{2}, 𝑦_{2)}, the slope between the two points is given by:

**COORDINATES OF A POINTS**

Example 1

- (5, 1) and (2,−2)
- (4,−2) and (−1, 0)
- (−2,−3) and (−4,−7)

**Solution**

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

**Solution**

**Equation of a Line**

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

**COORDINATES OF A POINTS**

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)

**Solution**

**COORDINATES OF A POINTS**

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

**Solution**

Intercepts

- to get 𝑥 − intercept, let 𝑦 = 0 and
- to get 𝑦 − intercept, let 𝑥 = 0

Example 5

**Solution**

**Graphs of Linear Equations**

- By using intercepts
- By using the table of values

**COORDINATES OF A POINTS**

Example 6

**Solution**

The Graph of a Linear Equation

**COORDINATES OF A POINTS**

**Simultaneous Equations**

equations.

**COORDINATES OF A POINTS**

Example 7

**Solution**

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