Question

Find the point which is two third of the way from p ( 0,1 ) to q ( 1,0)

Answer 1

Let the required point is R. Now R ins 2/3 away from P which means 
PR/PQ=2/3
or, PR/PR+RQ=2/3
or, 3PR=2PR+2RQ
or, 3PR-2PR=2RQ
or, PR=2RQ
or, PR/RQ=2/1
i.e., R intersects PQ at a ratio of 2:1.
If coordinate of R is (x,y) then
x=mx₂+nx₁/m+n and y=my₂+ny₁/m+n
where (x₁,y₁)=(0,1), (x₂,y₂)=(1,0) and m:n=2:1
∴, x=(2×1+1×0)/(2+1)
=2/3
y=(2×0+1×1)/(2+1)
=1/3
∴, coordinate of R is (2/3,1/3). Ans

Answer 2

Answer:

Let the required point is R. Now R ins 2/3 away from P which means

PR/PQ=2/3

or, PR/PR+RQ=2/3

or, 3PR=2PR+2RQ

or, 3PR-2PR=2RQ

or, PR=2RQ

or, PR/RQ=2/1

i.e., R intersects PQ at a ratio of 2:1.

If coordinate of R is (x,y) then

x=mx₂+nx₁/m+n and y=my₂+ny₁/m+n

where (x₁,y₁)=(0,1), (x₂,y₂)=(1,0) and m:n=2:1

∴, x=(2×1+1×0)/(2+1)

=2/3

y=(2×0+1×1)/(2+1)

=1/3

∴, coordinate of R is (2/3,1/3).

Step-by-step explanation:

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