A triangle is rotated $90$ degrees about the origin.
Which rule describes the transformation?

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Solution

A triangle is rotated $90$ degrees about the origin.
Concept used:
The rule for a rotation by $90$ degrees about the origin is $(x, y) \to (- y, x)$ .
See the in the diagram shown in below:
After $90 °$ rotation about the origin,
The point $A (3, 5)$ will be $A' (- 5, 3)$ .
The point $B (7, 5)$ will be $B' (- 5, 7)$ .
The point $C (5, 1)$ will be $C' (- 1, 5)$ .
Hence, the rule of the given transformation is $(x, y) \to (- y, x)$ .

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