Q1 of 184 Page 10

Find the coordinates of the point which divides the join of (-1,7) and (4,-3) internally in the ratio 2:3.

Let P(x,y) be the point which divides the line segment internally.

Using the section formula for the internal division, i.e.

…(i)

Here, m₁ = 2, m₂ = 3

(x₁, y₁) = (-1, 7) and (x₂, y₂) = (4, -3)

Putting the above values in the above formula, we get

⇒ x = 1, y = 3

Hence, (1,3) is the point which divides the line segment internally.

Prove, using coordinates that the sum of squares of the diagonals of a rectangle is equal to the sum of squares of its sides.

Find the coordinates of the point which divides the line segment joining (2,4) and (6,8) in the ratio 1:3 internally and externally.

Find the coordinates of the point which divides the line segment joining the points (4,-3) and (8,5) in the ratio 3:1 internally.

Find the coordinates of the points which trisect the line segment joining the points (2,3) and (6,5).