Question

triangle abc with vertices a(6, -6), b(2, 5), c(4, -3) is rotated 90° counterclockwise about the origin. what are the coordinates of triangle abc ?
a =

b =

c =

hint:
90° : (x, y) → (-y, x)
180°: (x, y) → (-x, -y)
270°: (x, y) → (y, -x)

Explanation:

Step1: Rotate Point A(6, -6)

Using the rule for 90° counterclockwise rotation \((x, y) \to (-y, x)\), substitute \(x = 6\) and \(y=-6\). So, \(-y = -(-6)=6\) and \(x = 6\). Thus, \(A'=(6, 6)\).

Step2: Rotate Point B(2, 5)

Using the same rule, substitute \(x = 2\) and \(y = 5\). Then, \(-y=-5\) and \(x = 2\). So, \(B'=(-5, 2)\).

Step3: Rotate Point C(4, -3)

Using the rule, substitute \(x = 4\) and \(y=-3\). Then, \(-y=-(-3)=3\) and \(x = 4\). So, \(C'=(3, 4)\).

Answer:

\(A' = (6, 6)\)
\(B' = (-5, 2)\)
\(C' = (3, 4)\)