Question

M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3. Find : 

1. co-ordinates of M
2. co-ordinates of P
3. length of BP

Answer 1

M is mid point of the line segment joining the points A(0, 4) and B(6, 0) M divides the line segment OP in the ratio 1 : 3

i. Now co-ordinates of M = `((0 + 6)/2, (4 + 0)/2) = (3, 2)`

ii. Let co-ordinates of P be (x, y), O is (0, 0)

`3 = (m_1x_2 + m_2x_1)/(m_1 + m_2)`

`3 = (1 xx x + 3 xx 0)/(1 + 3)`

= `(x + 0)/4`

= `x/4`

`=>` x = 12 and `2 = (1*y + 3 xx 0)/(1 + 3) = (y + 0)/4 = y/4`

∴ y = 2 × 4 = 8

∴ Co-ordinates of P are (12, 8)

iii. Length of BP = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

= `sqrt((2 - 6)^2 + (8 - 0)^2`

= `sqrt(6^2 + 8^2)`

= `sqrt(36 + 64)`

= `sqrt(100)`

= 10 units