The missing figure is attached below.
Answer:
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:
[tex](x,y)\to (-y,x)[/tex]
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:
[tex](x,y)\to (-y,x)[/tex]. 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.
