Question

how are the coordinates of a new point found the point is reflected through the x-axis? how are the coordinates of a new point found if the point is reflected through the y-axis​

Answer 1

If a point (x,y) or (-x,y) is reflected across the y-axis, you multiply x by -1, which instantly makes x a negative number or a positive number (depending is the number was already negative or positive). For example, if you have a point (2,7) and it's reflected across the y-axis, you need to multiply 2 by -1, which makes the point (-2,7). And if you have point (-3,6) you multiply the -3 by -1, which instantly takes the native sign off the -3 which makes (3,7). You do the same if a point is reflected across the x-axis. However you multiply y (not x) by -1.