Question

The coordinates of P and Q are (2,6) and (4,5) respectively. Equation of a line RS is Y= 2X -3. Determine if the lines are parallel or perpendicular

Answer 1

Perpendicular

Explanation:

Given points P=(2,6) and Q=(4,5)

The line RS is y=2x-3.

Now we know that the line joining any two points (x1,y1) and (x2,y2) has slope m=
`(y2-y1)/(x2-x1)`

Now the slope of the line PQ is

m1=
`(5-6)/(4-2)`= -
`(1)/(2)`

We know that the slope of the line in the form y=mx+c is m

So the line RS has slope m2=2

Now two lines are parallel if m1=m2

And those two lines are perpendicular if
`m1*m2=-1`

here m1= -
`(1)/(2)` and m2=2

clearly
`m1*m2=-1`

Therefore the two given lines are perpendicular