1.

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)

Answer»

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 = \(\frac{y_2-y_1}{x_2-x_1}\)

Now, The slope of the line whose Coordinates are (6, 3) and (1, 1)

⇒ m1 = \(\frac{1-3}{1-6}\) 

 ⇒ m1 =  \(\frac{-2}{-5}\) 

So, m1 = \(\frac{2}{5}\)

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

⇒ m2 = \(\frac{-5-5}{2+2}\) 

⇒ m2 = \(\frac{-10}{4}\)

So, m2 = \(\frac{-5}{4}\)

Here, m1m2 =  \(\frac{2}{5}\times-\frac{5}{2}\)

m1m2 = – 1 

Hence, The line is perpendicular to other. 


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