Question

Point s has coordinates 4,3. If you rotate s 90 degrees about the​ origin, (0,0), what are the coordinates of s​?

Answer 1

To rotate a point 90 degrees about the origin, use the rotation formulas x' = x*cos(q) + y*sin(q) and y' = -x*sin(q) + y*cos(q). Substituting the given coordinates (4,3) into these formulas, the new coordinates after rotation are (3, -4).

Step-by-step explanation:

To rotate a point 90 degrees about the origin, we can use the rotation formulas:

x' = x*cos(q) + y*sin(q)

y' = -x*sin(q) + y*cos(q)

In this case, the point S has coordinates (4,3). Substituting these values into the formulas, we get:

x' = 4*cos(90) + 3*sin(90) = 0 + 3 = 3

y' = -4*sin(90) + 3*cos(90) = -4 + 0 = -4

Therefore, the coordinates of S after rotating 90 degrees about the origin are (3, -4).

Answer 2

s' (- 3, 4 )

Step-by-step explanation:

under a rotation of 90° about the origin

a point (x, y ) → (- y, x ) , then

s (4, 3 ) → s' (- 3, 4 )