State whether the two lines through (5, 6) and (2, 3); through (9, – 2) and (6, – 5) are parallel, perpendicular or neither.

We have given Coordinates off two lines.

Given: (5, 6) and (2, 3); (9, – 2) and 96, – 5)

To Find: Check whether Given lines are perpendicular to each other or parallel to each other.

Concept Used: If the slopes of this line are equal the lines are parallel to each other. Similarly, If the product of the slopes of this two line is – 1, then lines are perpendicular to each other.

The formula used: Slope of a line, m =

Now, The slope of the line whose Coordinates are (5, 6) and (2, 3)

So, m₁ = 1

Now, The slope of the line whose Coordinates are (9, – 2) and (6, – 5)

So, m₂ = 1

Here, m_{1 =} m_{2 =} 1

Hence, The lines are parallel to each other.