Question

Prove: The segments joining the midpoints of the sides of a right triangle form a right triangle.

Segment PQ is perpendicular to segment RQ and Triangle PQR is a right triangle.

(fill in the blanks of the equation in the second picture with the correct number/letter/sign based off the first picture.)

Answer 1

P(a,0)
Q(a,b)
R(0,b)
Slope of PQ =(y(Q)-y(P))/((x(Q)-x(P))=(b-0)/(a-a)=b/0
slope of PQ =b/0 that means undefined
Slope of RQ=(y(Q)-y(R))/((x(Q)-x(R))=(b-b)/(a-0)=0/a=0

Answer 2

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:

`P=(a,0)`,

`Q=(a,b)`,

`R=(0,b)`.

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`

which are the required slope of PQ and RQ respectively.