Question

If PQRS is rectangle whose three vertices are P (0, 3), Q (0, 0), R (5, 0), then find the

length of its diagonal.​

Answer 1

Step-by-step explanation:

Given that the three vertices of a rectangle AOBC are

A(x

1

,y

1

)=(0,3),B(x

2

,y

2

)=(5,0) & O(x

3

,y

3

)=(0,0).

Now the abscissae of O and A are zeros.

So, OA falls along the Y axis.

Similarly, the ordinates of O and B are zeros.

So, OB falls along X−axis.

∴∠AOB=90

0

∴AB is a diagonal of AOBC.

Using distance formula, we have

AB=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

=

(5−0)

2

+(0−3)

2

units =

34

units.