Question

Tell weather the lines through the given points are parallel perpendicular or neither

Answer 1

Answer:

a)  Slope of line 1 = (2/3)

b)  Slope of line 2 = (-3/2)

c)  Two lines are perpendicular.

Step-by-step explanation:

Here, let the points of line 1 are A(1,0) and B(7,4)

Let the points of line 2 are A(7,0) and B(3,6)

Now for any two points,  the  slope m  of the line is given as :

$m = \frac{y_2 - y_1}{x_2-x_1}$

⇒Slope of the line AB  = $m1 =( \frac{4-0}{7-1}) = \frac{4}{6} = \frac{2}{3}$

or, m1  = 2/3

and Slope of the line PQ  = $m2 =( \frac{6-0}{3-7}) = -\frac{6}{4} = -\frac{3}{2}$

or, m2  = -3/2

Now, TWO LINERS ARE SAID TO BE PERPENDICULAR if

            m1 x  m2  = -1  :with heir respective slope m1 and m2

Here, $m1 \times m2 = \frac{2}{3} \times \frac{-3}{2} = -1$

⇒ SLOPE OF AB x SLOPE OF PQ  =   -1

Hence, Line AB is perpendicular to the line PQ.