Reflect (-3,7) across the x-axis then reflect across the y-axis. What are the coordinates of the final point?

Question

Plaese halp me!!

Answer 1

(-3,7) reflected across the x axis changes the sign of the y coordinate, to (-3,-7)

reflect that across the y axis changes the sign of the x coordinate to (3,-7)

just change the sign of both coordinates (--3,-7) = (3,-7)

it helps to graph the points

with two reflections across the axes

it's the same as drawing a line from the original point to the origin

then extend the line the same distance into quadrant IV

It's like a 180 degree rotation

you could rewrite the rectangular coordinates into polar

then rotate 180 degrees

then convert back to rectangular coordinates

(-3,7) = (sqr58, tan^-1(-7/3)) reflected rotates the angle 180 degrees

to (sqr58, tan^-1(-7/3) + 180)

then convert back to rectangular coordinates

= (3,-7)