**COORDINATES GEOMETRY OF STRAIGHT LINES**

CONTENT

- Distance between two points.
- Midpoint of line joining two points.
- Gradients and intercept of a straight line.
- Determination of equation of a straight line.
- Angle between two intersecting straight lines.
- 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.

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