Question

The point P(1, 2) divides the join of A(-2,1).
and B(7,4) in the ratio is :
(a) 1:2 (b) 2:1 (c) 3:1 (d) 1:3​

Answer 1

Answer:

Refer to the attachment :)✌️

Answer 2

The ratio in which P divides AB is 1:2. (Option a is correct)

Given,

Point P → (1, 2)

Point A → (-2, 1)

Point B → (7, 4)

To Find,

The ratio in which P divides AB

Solution,

Let the ratio be m₁:m₂

Thus, the point is given as -

x = $\frac{m1x2+m2x1}{m1+m2}$ ; y = $\frac{m1y2+m2y1}{m1+m2}$

Now we have been given the Point P → (1, 2), hence x = 1 and y = 2

Also, (x₁, y₁) = (-2, 1) and (x₂, y₂) = (7, 4)

1 = $\frac{7m1-2m2}{m1+m2}$ ; 2 = $\frac{4m1+m2}{m1+m2}$

m₁ + m₂ = 7m₁ - 2m₂

6m₁ - 3m₂ = 0

2m₁ = m₂              

$\frac{m1}{m2} = \frac{1}{2}$

Thus we get the ratio as 1:2

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