Triangle PQR where P(1,4), Q(-3,-4),R(7,k) is right-angled at Q. find the value of k

k = - 9

Step-by-step explanation:

Since the triangle is right- angled at Q then PQ is perpendicular to RQ

Calculate the slope of PQ using the slope formula

m =

with (x₁, y₁ ) = P(1, 4) and (x₂, y₂ ) = Q(- 3, - 4)

= = = 2

Given a line with slope m then the slope of a line perpendicular to it is

= - = - , thus

= -

Calculate the slope of RQ and equate to -

= = - , that is

= - ( multiply both sides by 10 )

k + 4 = - 5 ( subtract 4 from both sides )

k = - 9

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.