1.

State whether the two lines in each of the following are parallel, perpendicular or neither : Through (3, 15) and (16, 6); through (– 5, 3) and (8, 2)

Answer»

We have given Coordinates off two line. 

Given: (3, 15) and (16, 6) and (– 5, 3) and (8, 2) 

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

Now, 

Concept Used: If the slopes of these line are equal the the lines are parallel to each other. Similarly, If the product of the slopes of these 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 (3, 15) and (16, 6)

⇒ m1 = \(\frac{6-15}{16-3}\) 

 ⇒ m1 =  \(\frac{-9}{13}\) 

So, m1 = \(\frac{-9}{13}\)

⇒ m2 = \(\frac{2-3}{8-(-5)}\) 

⇒ m2 = \(\frac{-1}{13}\)

So, m2 = \(\frac{-5}{2}\)

Here, m1≠m2 nor m1m2 = – 1 

Hence, The lines are neither perpendicular and nor parallel to each other.


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