You need to determine the coordinates of the point` A` , hence, you need to use the information provided by the problem that the point `A` lies on the line `x + y + m = 0` .

Since the point `A` lies of the given line, you need to plug its coordinates into the line equation such that:

`x_A + y_A + m = 0 => m^2 + m + m = 0 => m^2 + 2m = 0`

Factoring out `m` , yields:

`m(m + 2) = 0`

Using the zero product rule yields:

`m = 0`

`m + 2 = 0 => m = -2`

**Hence, evaluating m yields that the line `x + y = 0` passes through the origin `(0,0)` and the line `x + y - 2 = 0` passes through the point `(4,-2)` .**

x+y+m =0

y = -x-m

A has the coordinates x=m^2, y=m

Therefore

m = -m^2 -m

m^2+2m =0

m(m+2) =0

the solutions are m1=0 and m2 =-2

therefore the point A is (0,0) or A is (4,-2).