Question

Line joining the points (3, -4) and (-2, 6) is perpendicular to the line joining the points (-3, 6) and (9 -18).(True or False)
please explain your answer

Answer 1

Answer:

The answer is FALSE

Step-by-step explanation:

we know from the concept of slope, that :

    >if two lines have same slope, then those lines are parallel or overlapped lines

and,

   >if the multiplication of the slopes of the two lines is ( -1 ), then those lines are perpendicular

         i.e. m₁ * m₂ = -1  

Now, calculating slopes by, slope formula:

          $m =\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

therefore,

$m_{1} = \frac{(6) - (-4)}{(-2) - (3)} = \frac{10}{(-5)} = -2$

$m_{2} = \frac{(-18)-(6)}{(9)-(-3)} = \frac{(-24)}{12} = -2$

Hence, the slopes are same.

Therefore the the lines are parallel or overlapped BUT NOT Perpendicular