Q16 of 157 Page 757

In what ratio does the point C(4, 5) divide the join of A(2, 3) and B(7, 8)?

Let the ratio in which the point C(4, 5) divide the join of A(2, 3) and B(7, 8) be m:n.

Recall that if (x,y) ≡ (a,b) then x = a and y = b

Let (x,y) ≡ (4,5)

(x₁,y₁) ≡ (2,3)

and, (x₂,y₂) ≡ (7,8)

Now, Using Section Formula-

⇒ 4m + 4n = 7m + 2n

⇒ 3m = 2n

∴ m:n = 2:3

Thus, the required ratio is 2:3.

If the centroid of ΔABC having vertices A(a, b), B(b, c) and C(c, a) is the origin, then find the value of (a + b + c).

Find the centroid of ΔABC whose vertices are A(2, 2), B(-4, -4) and C(5, - 8).

If the points A(2, 3), B(4, k) and C(6, -3) are collinear, find the value of k.

The distance of the point P(-6, 8) from the origin is