Question 20.11.4: If the origin be shifted to the point (3,-1), find the new e......
If the origin be shifted to the point (3,-1) , find the new equation of the line 2 x-3 y+5=0 .
Step-by-Step
Let the origin O be shifted to the point O^{\prime}(h, k) , where h=3 and k=-1 .
Let the new coordinates of P(x, y) be P\left(x^{\prime}, y^{\prime}\right) .
Then, x^{\prime}=x-h \Rightarrow x^{\prime}=x-3 \Rightarrow x=x^{\prime}+3 .
And, y^{\prime}=y-k \Rightarrow y^{\prime}=y+1 \Rightarrow y=y^{\prime}-1 .
So, the new equation becomes:
2\left(x^{\prime}+3\right)-3\left(y^{\prime}-1\right)+5=0 \Rightarrow 2 x^{\prime}-3 y^{\prime}+14=0 \text {. }Hence, the equation of the straight line in the new system is 2 x-3 y+14=0 .
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