Question

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

Answer 1

a) Slope of line 1 = (2/3)

b) Slope of line 2 = (-3/2)

c) Two lines are perpendicular.

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 = (y_2 - y_1)/(x_2-x_1)`

⇒Slope of the line AB =
`m1  =( (4-0)/(7-1))  = (4)/(6)    = (2)/(3)`

or, m1 = 2/3

and Slope of the line PQ =
`m2  =( (6-0)/(3-7))  = -(6)/(4)    = -(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 * m2  = (2)/(3) * (-3)/(2)   = -1`

⇒ SLOPE OF AB x SLOPE OF PQ = -1

Hence, Line AB is perpendicular to the line PQ.