If we take a point (x,y) and rotate it 180 degrees about the origin, the two coordinates change sign. That is, the point (x,y) becomes (or moves to) (-x,-y).
If you then take that point which is now (-x,-y) and translate it (slide it over) 4 units left you are taking the x-coordinate and moving it left 4 which is taking the x-coordinate and subtracting 4. The point (-x,-4) when you subtract 4 from the -x becomes (-x-4,-y)
So the two transformations (rotation of 180 degrees followed by a translation 4 units left) take a point (x,y) and move it to its image (-x-4,-y)
Now we are asked for the image of point P. The coordinates of P can be found from the diagram. If you start at the origin (where the x and y axis cross or the center of the plane you are given) to travel to P you move 5 units right and 2 units up. That is, the coordinates of P are (5,2)
So for P (x,y) = (5,2)
The image of P is (-x-4,-y) which is (-5-4, -2). That is, the image of P is (-9,-2)
Answer: Sound waves entering a warmer air means that the kinetic energy of the air particles will increase and thus the vibration of particles will be increased and thus the speed of transmission of sound waves increases.
