Question

What is the image point of (8,9) after the transformation T 1,2 O R270?

a) (7,10)
b) (-9,8)
c) (-10,-7)
d) (9,-8)

Answer 1

The image point of (8,9) after the transformation T 1,2 O R270 is (-8,-1).

Step-by-step explanation:

The transformation T 1,2 O R270 represents a rotation of 270 degrees counterclockwise about the origin (0,0) in the coordinate plane. To find the image point of (8,9) after this transformation, we need to apply the rotation formula. First, perform the rotation by substituting the coordinates of the point with their respective formulas:

x' = x*cos(theta) - y*sin(theta)

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

Substituting the values in, we get:

x' = (8*cos(270)) - (9*sin(270))

y' = (8*sin(270)) + (9*cos(270))

Performing the calculations:

x' = (-8) - (9*0) = -8

y' = (8*1) + (9*(-1)) = -1

Therefore, the image point of (8,9) after the transformation T 1,2 O R270 is (-8,-1).