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If the mid point between the points $(a+b, a-b)$ and $(-a, b)$ lies on the line $a x+b y=k$, what is $k$ equal to?
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The correct answer is:
ab
Given points are $(a+b, a-b)$ and $(-a, b)$ Mid point is $\left(\frac{a+b-a}{2}, \frac{a-b+b}{2}\right)=\left(\frac{b}{2}, \frac{a}{2}\right)$
Since, it lies on $a x+b y=k$ $a\left(\frac{b}{2}\right)+b\left(\frac{a}{2}\right)=k \Rightarrow k=a b$
Since, it lies on $a x+b y=k$ $a\left(\frac{b}{2}\right)+b\left(\frac{a}{2}\right)=k \Rightarrow k=a b$
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