Question

Two of the vertices of ΔPQR are P(−1, 5) and Q(5, 2). The coordinates of a point which divides PQ in the ratio 2 : 1 are ______.

Options

• (3, −3)

• (5, 5)

• (3, 3)

• (5, 1)

Answer 1

Two of the vertices of ΔPQR are P(-1, 5) and Q(5, 2). The coordinates of a point which divides PQ in the ratio 2 : 1 are (3, 3).

Explanation:

m : n = 2 : 1

(x₁, y₁) = (−1, 5)

(x₂, y₂) = (5, 2)

x = `(mx_2+nx_1)/(m+n)`

= `(2xx5+1xx-1)/(2+1)`

= `(10-1)/3`

= `9/3`

= 3

y = `(my_2+ny_1)/(m+n)`

= `(2xx2+1xx5)/(2+1)`

= `9/3`

= 3