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

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 \(A(9,-2)\), swap \(x = 9\) and \(y=-2\). So \(A'\) is \((-2,9)\).

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

For \(B(6,3)\), swap \(x = 6\) and \(y = 3\). So \(B'\) is \((3,6)\).

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

For \(C(-2,-6)\), swap \(x=-2\) and \(y = -6\). So \(C'\) is \((-6,-2)\).

Answer:

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