State whether the two lines in each of the following are parallel, perpendicular or neither :
Through (6, 3) and (1,1); through (– 2, 5) and (2, – 5)
We have given Coordinates off two line.
Given: (6, 3) and (1,1) and (– 2, 5) and (2, – 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 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 (6, 3) and (1, 1)
So, m1 =
Now, The slope of the line whose Coordinates are (– 2, 5) and (2, – 5)
So, m2 =
Here, m1m2 =
m1m2 = – 1
Hence, The line is perpendicular to other.