1.

State whether the two lines in each of the following are parallel, perpendicular or neither : Through (5, 6) and (2, 3); through (9, – 2) and (6, – 5)

Answer»

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 = \(\frac{y_2-y_1}{x_2-x_1}\)

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

⇒ m1 = \(\frac{3-6}{2-5}\) 

 ⇒ m1 =  \(\frac{-3}{-3}\) 

So, m1 = 1

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

⇒ m2 = \(\frac{-5-(-2)}{6-9}\) 

⇒ m2 = \(\frac{-3}{-3}\)

So, m2 = 1 

Here, m1 = m2 = 1 

Hence, The lines are parallel to each other.


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