Question

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

(–6, 10)
(–4, –8)
(0, –1)
(2, 4)

Answer 1

Answer is -4,-8 as said already

Answer 2

Answer: (–4, –8)

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 = (2-b)/(4-a)`

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

`m_2 = (-4-4)/(4-(-6)) = (-8)/(4+6) = (-8)/(10) = (-4)/(5)`

Since, both lines are perpendicular to each other,

⇒
`m_1* m_2=-1`

⇒
`(2-b)/(4-a)* (-4)/(5) = - 1`

⇒
`(4(2-b))/(5(4-a)) = 1`

⇒
`(8-4b)/(20-5a) =1`

⇒
`8-4b = 20 - 5a`

⇒
`5a-4b=12` ---------(1)

For, a = -6 and b = 10,

`5* -6-4* 10=-70\\eq 12`

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

`5* -4-4* -8=12= 12`

For, a = 0 and b = -1,

`5* 0-4*-1=4\\eq 12`

For, a =2 and b = 4,

`5* 2-4* 4=-6\\eq 12`

⇒ Second Option is correct.