Question

find the new coordinates after rotating triangle cde with vertices c(2, 4), d(6, 7), and e(7, 3): 90°

Explanation:

Step1: Recall 90° rotation rule

The rule for rotating a point \((x, y)\) 90° counterclockwise about the origin is \((x, y) \to (-y, x)\). For clockwise, it's \((x, y) \to (y, -x)\). Assuming counterclockwise (standard unless stated), we use \((-y, x)\).

Step2: Rotate point C(2, 4)

Apply the rule: \(x = 2\), \(y = 4\). New coordinates: \((-4, 2)\).

Step3: Rotate point D(6, 7)

Apply the rule: \(x = 6\), \(y = 7\). New coordinates: \((-7, 6)\).

Step4: Rotate point E(7, 3)

Apply the rule: \(x = 7\), \(y = 3\). New coordinates: \((-3, 7)\).

If clockwise, the rule is \((y, -x)\):

• C(2,4) → (4, -2)
• D(6,7) → (7, -6)
• E(7,3) → (3, -7)

Since the problem doesn't specify direction, but 90° rotation (often counterclockwise in math unless stated). Let's confirm counterclockwise:

For counterclockwise 90°:

• C(2,4) becomes (-4, 2)
• D(6,7) becomes (-7, 6)
• E(7,3) becomes (-3, 7)

Answer:

If rotating 90° counterclockwise about the origin:
C'(-4, 2), D'(-7, 6), E'(-3, 7)

If rotating 90° clockwise about the origin:
C'(4, -2), D'(7, -6), E'(3, -7)

(Assuming counterclockwise as standard, the new coordinates are C'(-4, 2), D'(-7, 6), E'(-3, 7))