Question

If A and B be the points (1.5) and (-4,7) then find the point P which divides AB internally in the ratio 2:3.

Answer 1

Answer:

The point p is (-11/5, 11/5)

Answer 2

The point P which divides AB internally in the ratio 2:3 is  (-1, 19/5 )

Given:

A and B be the points (1,5) and (-4,7)

The ratio that P divides AB = 2:3

To find:

The point P which divides AB internally in the ratio 2:3.

Solution:

NOTE:

The formula for a point P which divides line formed by (x₁, y₁) and (x₂, y₂) in ration m:n is given by  

          [mx₂+nx₁ /m+n,   my₂+ny₁ / m+n]

From given data the points are A(1,5) and B(-4,7) and Ratio m : n = 2:3

The required point P = [(2)(-4)+3(1) /2+3,   2(7)+3(5) / 2+3]  

= [ -8+3/5,  14+15/5 ]

= [ -5/5,  19/5 ]

= (-1, 19/5 )

Therefore,

The point P which divides AB internally in the ratio 2:3 is  (-1, 19/5 )

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