Question

triangle abc was transformed using the rule $(x,y)\
ightarrow(-y,x)$. the vertices of the triangles are shown.
$a(-1,1)$ $a(-1,-1)$
$b(1,1)$ $b(-1,1)$
$c(1,4)$ $c(-4,1)$
which best describes the transformation?
the transformation was a $90^{circ}$ rotation about the origin.
the transformation was a $180^{circ}$ rotation about the origin.
the transformation was a $270^{circ}$ rotation about the origin.
the transformation was a $360^{circ}$ rotation about the origin.

Explanation:

Step1: Recall rotation rules

• \(90^{\circ}\) counter - clockwise rotation about the origin: \((x,y)\to(-y,x)\)
• \(180^{\circ}\) rotation about the origin: \((x,y)\to(-x,-y)\)
• \(270^{\circ}\) counter - clockwise rotation about the origin: \((x,y)\to(y, - x)\)
• \(360^{\circ}\) rotation about the origin: \((x,y)\to(x,y)\)

Step2: Compare the given rule with rotation rules

The given transformation rule is \((x,y)\to(-y,x)\), which matches the rule for a \(90^{\circ}\) counter - clockwise rotation about the origin.

Answer:

The transformation was a \(90^{\circ}\) rotation about the origin.