1.

Point P (h,k) divides a line segment between the exes in the ratio 1:2 Find the lengths (intercepts) on the axes made by this segment. Also find the area of triangle formed by the line segment and the axes.

Answer»

Solution :Let AB be the line segment joining A (0.y) and B (x,0) between the axes.
P (h,k) divides the line segment in the ratio `1:2.`
Now, question arises that whether `PA:PB=1:2` or `PB:PA=1:2` or `PB:PA = 1:2`
The answer of this is that always we take the FORMER part of ratio towards the X-axis and latter part of ratio towards the Y-axis.

So, here we will take
`""PB,PA=1:2`
`THEREFORE` By using section FORMULA,
`h=(1(0)+2(x))/(1+2)implies""h=(2x)/(3)impliesx=(3H)/(2)`
and `k=(1(y)+2(0))/(1+2)implies""k=(y)/(3)impliesy=3k`
So, length of intercept on the X-axis `=OB=x=(3h)/(2)`
and the length of intercept on the Y-axis =OA = y = 3k.
`therefore` Area of `DeltaAOB=1/2xxOBxxOA=1/2(3h)/(2)xx3k=9/4hk` SQUARE units


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