Which image shows a counter-clockwise rotation of the blue quadrilateral pqrs 90° around the origin?

The missing figure is attached below.

The first image from left.

Step-by-step explanation:

Given:

Rotation of the quadrilateral PQRS by 90 degree counterclockwise around the origin.

We know that, for a 90 degree counterclockwise rotation, the transformation rule for the coordinates is given as:

So, the 'x' and 'y' interchange their values after rotation and the 'y' value sign is reversed.

Now, let us check each option.

Option 1:

Coordinates of the original quadrilateral are:

P(5, 2.5), Q(1, 4), R(2, 2.5), and S(1, 1)

Now, after rotation by 90 degree counterclockwise, the coordinates of the transformed figure will be:

. So,

P(5, 2.5) → P'(-2.5, 5)

Q(1, 4) → Q'(-4, 1)

R(2, 2.5) → R'(-2.5, 2)

S(1, 1) → S'(-1, 1)

Now, if we check the coordinates of P', Q', R' and S' on the first option, we see that they are same as calculated above. So, the correct option is option 1.

Option 2:

Coordinates of P are (5, 2.5) and coordinates of P' are (2.5, -5) which doesn't match with the transformation rule. So, this option is incorrect.

Option 3:

Coordinates of P are (5, 2.5) and coordinates of P' are (-5, 2.5) which doesn't match with the transformation rule. So, this option is incorrect.