coordinates of (-6,5) when rotated 180 degrees

Answer 1

(-6,5) becomes (6,-5) when rotated 180 degrees,

just change the signs of both coordinates, same as reflecting across the x axis and across the y axis

draw a rough sketch of the point on a piece of paper and rotate the paper 180 degrees (clockwise or counterclockwise) and see what happens. you get a point symmetrical across the origin

or another method is convert to polar coordinates

(-6,5) in polar = (sqr61, arctan(-5/6)) now add (or subtract 180 from arctan(-5/6)

to get

(sqr61, 140.2+180) = (sqr61, 320.2), approximately, rounding off

now convert back to rectangular coordinates

for polar (r,T) the counterpart is (rcosT, rsinT) r^2 = x^2 + y^2= 6^2 +5^2 = 36+25 = 61, r =sqr61

sqr61(sin320.2)= -5

sqr61(cos320.2) = 6

(sqr61,3202)= (6,-5)= same point as earlier above by just switching both signs of the original point

polar coordinates do make it a little unnecessarily complicated, but it shows the angle rotation better