Question

given a(9, - 2), b(6,3), and c(-2,-6), what are the coordinates of the vertices of triangle abc after a reflection over the line y = x?
a(type your answers as an ordered pair in parentheses).
b
c

Explanation:

Step1: Recall the reflection rule over \(y = x\)

When reflecting a point \((x,y)\) over the line \(y=x\), the rule is \((x,y)\to(y,x)\).

Step2: Apply the rule to point \(A(9, - 2)\)

For \(A(9,-2)\), using the rule \((x,y)\to(y,x)\), we get \(A'(-2,9)\).

Step3: Apply the rule to point \(B(6,3)\)

For \(B(6,3)\), using the rule \((x,y)\to(y,x)\), we get \(B'(3,6)\).

Step4: Apply the rule to point \(C(-2,-6)\)

For \(C(-2,-6)\), using the rule \((x,y)\to(y,x)\), we get \(C'(-6,-2)\).

Answer:

\(A'(-2,9)\), \(B'(3,6)\), \(C'(-6,-2)\)