Question

A line meets the co-ordinate axes at the points A and B respectively. If P (6,3) divides seg AB in the ratio 1:3,find the equation of the line.
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Answer 1

Answer:

A)

Toolbox:

Section formula : The coordinates of the point which divides the line joining the points (x1,y1)(x1,y1) and (x2,y2)(x2,y2) in the ratio m:nm:n is (mx2+nx1m+n(mx2+nx1m+n,my2+ny1m+n),my2+ny1m+n)

Step 1 :

Let the equation of the line be xaxa+yb+yb=1=1.

The line meets the coordinate axes at A(a,0)A(a,0) and B(0,b)B(0,b) respectively. The coordinates of the point which divides the line joining A(a,0)A(a,0) and B(0,b)B(0,b) in the ratio 1:21:2 are

(1×0+2×a1+2(1×0+2×a1+2,1×b+2×01+2),1×b+2×01+2)

⇒(2a3⇒(2a3,b3),b3)

It is given that the point (-5, 4) divides AB in the ratio 1 : 2

∴2a3∴2a3=−5andb3=−5andb3=4=4

(i.e) a=−152a=−152 and b=12b=12

Step 2 :

Hence the equation of the required line is

x−152x−152+y12+y12=1=1

⇒2x−15⇒2x−15+y12+y12=1=1

⇒24x+15y=−180⇒24x+15y=−180

or 8x+5y−60=0

Answer 2

Answer:

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