Question

Complete the following proof.Prove: The segments joining the midpoints of the sides of a right triangle. If the answer is undefined use the letter U.

Answer 1

Explanation:

From the given figure, it can be seen that the coordinates of the given points are:

`A=(0,0),B=(2a,0),A=(0,2b),P=(a,0),Q=(a,b),R=(0,b)`

Now, The coordinates of P, Q and R are:

`\begin{gathered} P=(a,0) \\ Q=(a,b) \\ R=(0,b) \end{gathered}`

Now, slope of PQ is given as:

`S=(b-0)/(a-a)=(b)/(0)`

which is undefined.

Slope of RQ is given as:

`S=(b-b)/(a-0)=(0)/(a)=0`

which are the required slope of PQ and RQ respectively.