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# COORDINATES GEOMETRY OF STRAIGHT LINES

CONTENT

1. Distance between two points.
2. Midpoint of line joining two points.
3. Gradients and intercept of a straight line.
4. Determination of equation of a straight line.
5. Angle between two intersecting straight lines.
6. Application of linear graphs to real life situation.

## DISTANCE BETWEEN TWO POINTS

Let $$P_1(x_1, y_1)$$ and $$P_2(x_2, y_2)$$ be two distinct points. The distance d between them can thus be calculated.

Applying Pythagoras theorem to right- angled triangle in the graph above,

$$d^2 = (x_2 -x_1)^2 + (y_2 -y_1)^2 \\ d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2 }$$

Example 1:

Calculated the distance between the points, (4, 1) and (3, −2)

Solution:

The distance between the points (4, 1) and (3, −2) is

$$\sqrt{[(4 -3)^2 + (1 -(-2))^2 ]} \\ \sqrt{10} = 3.16$$

EXAMPLE 2:

Find the length of the line segment with end points (2,8) and (6,5).

Solution:

$$X_1 = 2, Y_1 = 8, X_2 = 6, Y_2 = 5 \\ d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2 } \\ d = \sqrt{(6 -2)^2 + (5 -8)^2 } \\ d = \sqrt{4^2 + (-3)^2 } \\ d = \sqrt{25} \\ d = 5$$

CLASS  ACTIVITY

Find the distances between the given points:

1.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS2 General Mathematics, SS2 General Mathematics Evaluation Questions, SS2 General Mathematics Evaluation Questions First Term, SS2 General Mathematics First Term, SS2 General Mathematics Objective Questions, SS2 General Mathematics Objective Questions First Term
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