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Question

If P(9a2,b) divides the line segment joining A(3a+1,2) and B(8a,5) in the ratio 3:1.

Find the value of a and b.


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Solution

Find the value of a and b

Given that, P divides the line segment AB in the ratio of 3:1

A(3a+1,-2)=(x1,y1) write in the format A(x,y)=(a,b)

B(8a,5)=(x2,y2)

m:n=3:1

m+n=4

Section formula is used in coordinate geometry to calculate the ratio in which a line joined by two points can be divided.

Use the section formula,

x=mx2+nx1m+nand y=my2+ny1m+n

Now, substitute the known values in the formula

x=38a+13a+14 and y=35+1-24

x=(24a+3a+1)4 and y=15-24

Now find the value of a:

9a-2=27a+1436a-8=27a+19a=9a=1

Now find the value of b

-b=134b=-134

Hence the value of a is 1 and b is -134.


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