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

Answer:

Perpendicular

Step-by-step 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=$\frac{y2-y1}{x2-x1}$

Now the slope of the line PQ is

m1=$\frac{5-6}{4-2}$= -$\frac{1}{2}$

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= -$\frac{1}{2}$    and m2=2

clearly $m1*m2=-1$

Therefore the two given lines are perpendicular