Question

[][]Note to teacher:

Note from teacher:


A pre-image point is rotated 270° clockwise. If the pre-image point had the coordinates (3, -5), what are the coordinates of its image point?

Answer 1

convert (3,-5) into a polar coorinate; rotate, and then undo back into rectangular coords

Answer 2

or simply since this is a perpendicular we could determine the slope equation and translate into the perp

Answer 3

but polars is the route to go, a little simpler

Answer 4

given (x,y) convert to (r,t), and rotate to (r,t1)

r = sqrt(3^2+5^2) = sqrt(34)

t = tan-1(-5/3)
t1 = tan-1(-5/3) - 270, make sure we stay in degrees

convert back to rectangulars: (x1,y1)

x1 = r cos(t1)
y1 = r sin(t1)

Answer 5

t1 = 30.96 degrees if i did it right

x1 = about 5
y1 = about 3 ..

Answer 6

which is what youd expect from a perpendicular arrangment like this;

<3,-5> perps to <5,3>; from origin that equals (5,3)

Answer 7

great work amistre 64 , !!!