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

Answer:

Step-by-step 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:

$S=\frac{b-0}{a-a}= \frac{b}{0}$

which is undefined.

Slope of RQ is given as:

$S=\frac{b-b}{a-0}=0$

which are the required slope of PQ and RQ respectively.