PUMPA - THE SMART LEARNING APP

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Download now on Google Play### Theory:

Let us look at the following graph:

Let the mid-point be \(M\) with the vertex \(M(x\), \(y)\).

From the similarity property, it is understood that \(\triangle{AMM'}\) and \(\triangle{MDB}\) are similar.

This makes the two corresponding sides equal.

Therefore, the ratio between the two corresponding sides are also equal.

\(\frac{AM'}{MD} = \frac{MM'}{BD} = \frac{AM}{MB} = \frac{1}{1}\)

We know that since \(M\) is the mid-point of \(AB\), \(AM = MB\).

So, \(\frac{x - x_1}{x_2 - x} = \frac{y - y_1}{y_2 - y} = \frac{1}{1}\)

Let us only consider \(\frac{x - x_1}{x_2 - x} = \frac{1}{1}\)

\(x - x_1 = x_2 - x\)

\(2x = x_1 + x_2\)

\(x = \frac{x_1 + x_2}{2}\)

Similarly \(y\) becomes \(\frac{y_1 + y_2}{2}\)

\(y = \frac{y_1 + y_2}{2}\)

Hence, the mid-point be \(M\) with the vertex \(M(x\), \(y)\) becomes \(M(\frac{x_1 + x_2}{2}\), \(\frac{y_1 + y_2}{2})\).