Square PQRS is transformed as shown on the graph. Which rule describes the transformation?
Ra 90°
Ro, 180°
O RO, 270
O Ro 360
S

The rule that describes this transformation is R₀ 270°

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

If a point A(x, y) is rotated clockwise by 270 degrees, the new point is at A'(-y, x)

Quadrilateral PQRS is at P(-3, 5), Q(-1, 3), R(-3, 1) and S(-5, 3). If PQRS is rotated 270 degrees clockwise, the new point is at P'(-5, -3), Q'(-3, -1), R'(-1, -3) and S'(-3, 5)

Find out more on transformation at: link

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!