Andrew did not provide enough information!

Geometry Level 3

Andrew was playing with a line having the equation: $ax+by+c=0$ . He reflected a certain point having co-ordinates $(m,n)$ on that line and found that the co-ordinates of the new point were $(n,m)$ .

Andrew was intrigued by this and challenged his friends to find the value of $a+b$ .So, what is the value of $a+b$ ?

Clarification: The point $(m,n)$ does not lie on Andrew's line.

The answer is 0.0.

1 solution

Adarsh Kumar
Mar 23, 2016

We see that the line $ax+by+c=0$ has slope $m_1=\dfrac{-a}{b}$ hence the line joining the points $(m,n),(n,m)$ has slope $m_{2}=\dfrac{b}{a}$ as $m_1 \times m_2=-1$ ,but then, $\dfrac{n-m}{m-n}=\dfrac{b}{a}$ hence $\color{#D61F06}{a+b=0}$ .And done!

Yep , as simple as that. +1

Nihar Mahajan - 5 years, 2 months ago

Yup!Keep posting CG probs $:)$

Adarsh Kumar - 5 years, 2 months ago

Andrew did not provide enough information!

The answer is 0.0.

1 solution

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