triangle abc was transformed using the rule (x, y)→(-y, x). the vertices of the triangles are shown. a(-1…

Answer:

The transformation was a 270° rotation about the origin.

Explanation:

Step1: Recall rotation rules

For a 90 - degree rotation about the origin, the rule is $(x,y)\to(-y,x)$. For a 180 - degree rotation, $(x,y)\to(-x,-y)$. For a 270 - degree rotation, $(x,y)\to(y, - x)$. For a 360 - degree rotation, $(x,y)\to(x,y)$.

Step2: Analyze given rule

The given rule is $(x,y)\to(-y,x)$. This is the rule for a 270 - degree counter - clockwise rotation about the origin. We can also check with the vertices: For point $A(-1,1)$, applying the rule $(x,y)\to(-y,x)$ gives $A'(-1,-1)$. For point $B(1,1)$, applying the rule gives $B'(-1,1)$. For point $C(1,4)$, applying the rule gives $C'(-4,1)$. So the transformation is a 270 - degree rotation about the origin.