1.

State whether the two lines in each of the following are parallel, perpendicular or neither : Through (9, 5) and (– 1, 1); through (3, – 5) and (8, – 3)

Answer»

We have given Coordinates off two line. 

Given: (9, 5) and (– 1, 1); through (3, – 5) and (8, – 3) 

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 (9, 5) and (– 1, 1)

⇒ m1 = \(\frac{1-5}{-1-9}\) 

⇒ m1 = \(\frac{-4}{-10}\)  

So, m1 = \(\frac{2}{5}\)

Now, The slope of the line whose Coordinates are (3, – 5) and (8, – 3)

⇒ m2 = \(\frac{-3-(-5)}{8-3}\) 

⇒ m2 = \(\frac{2}{5}\)

So, m2 = \(\frac{2}{5}\) 

Here, m1 = m2 = \(\frac{2}{5}\)

Hence, The lines are parallel to each other.


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