Question

A straight line meets the axes at A and B such that the centroid of triangle OAB is (a,a). the equation of the line AB is

Answer 1

Please see the attachment

Answer 2

Given,

A straight line meets the axes at A and B.

The centroid od triangle OAB is (a, a)

To Find,

The equation of line AB.

Solution,

Let the coordinate of point A be (p,0) and B be (0,q)

Now,

The formula for calculating the centroid of the triangle is

Centroid = [(x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3]

(a,a) = [(0+0+p)/3, (0+q+0)/3]

p = 3a and q = 3a

Now, the equation of line AB will be

(y-0) = (3a-0)*(x-3a)/(0-3a)

y = -(x-3a)

x+y-3a = 0

Hence, the equation of line AB is x+y-3a = 0.