Question

Which point is on the line that passes through point R and is perpendicular to line PQ?

Answer 1

Answer: (–4, –8)

Step-by-step explanation:

Let the coordinates of common point of the given lines are (x,y),

Thus, the slope of the line passes through the points (a,b) and R(4,2) is,

$m_1 = \frac{2-b}{4-a}$

Again, the slope of the line passes through two points P(-6,4) and Q(4,-4),

$m_2 = \frac{-4-4}{4-(-6)} = \frac{-8}{4+6} = \frac{-8}{10} = \frac{-4}{5}$

Since, both lines are perpendicular to each other,

⇒ $m_1\times m_2=-1$

⇒ $\frac{2-b}{4-a}\times \frac{-4}{5} = - 1$

⇒  $\frac{4(2-b)}{5(4-a)} = 1$

⇒  $\frac{8-4b}{20-5a} =1$

⇒  $8-4b = 20 - 5a$

⇒  $5a-4b=12$    ---------(1)

For, a = -6 and b = 10,

$5\times -6-4\times 10=-70\neq 12$  

For, a = -4 and b = -8,

$5\times -4-4\times -8=12= 12$  

For, a = 0 and b = -1,

$5\times 0-4\times-1=4\neq 12$  

For, a =2 and b = 4,

$5\times 2-4\times 4=-6\neq 12$  

⇒ Second Option is correct.

Answer 2

Answer is -4,-8 as said already