The coordinates of point a on a coordinate grid are (−2, −3). point a is reflected across the y-axis to obtain point b and across the x-axis to obtain point c. what are the coordinates of points b and c?

A reflection is a common type of transformation. To reflect a point across the x-axis, we consider this axis to be a mirror. On the other hand, if you want to reflect a point across the y-axis, you need to consider this axis to be a mirror. A coordinate grid is the rectangular coordinate system. Just as we can represent real numbers by points on a real number line, we can represent ordered pairs of real numbers by points in a plane called the rectangular coordinate system, or the Cartesian plane. So:

If you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate changes into its opposite. So, if we have a point , the reflection of this point across  the x-axis is the point . Finally, our point A changes into:

Point B:

If you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate changes into its opposite. So, if we have a point , the reflection of this point across  the y-axis is the point . Finally, our point A changes into:

Point C:

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answer: i think it is (1,-2)

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!