Two straight lines intersect at a single point (*x, y*). The point satisfies the equations of both lines. We find this point by solving simultaneous equations.

Concurrent lines meet a single point. To show that lines are concurrent, solve two simultaneous equations to find the point of intersection. Then substitute this point of intersection into the third and subsequent lines to show that these lines also pass through the point.

### Examples:

1. Find the point of intersection between lines and .

### Show Answer

2. Show that the lines , and are concurrent.

### Show Answer

## Perpendicular Distance

Perpendicular distance is used to find the distance between a point and a line. If we look at the distance between a point and a line, there could be many distances.

So we choose the shortest distance, which is the perpendicular distance.

The perpendicular distance from to the line is given by:

### Examples:

1. Find the perpendicular distance of (4, -3) from the line .

### Show Answer

2. Prove that the line is a tangent to the circle .

### Show Answer

In this problem, we know the circle has the origin has a radius of units, which should be the perpendicular distance if the statement above had been true. Therefore, we prove that the perpendicular distance from the line to the origin is 2 units.

**IF** the distance is not 2 units, which implies that the perpendicular distance is either more or less than the radius, the line is NOT tangent to the circle.