Question

write the coordinates of the vertices after a reflection over the line $y = x$.

$b( , )$
$c( , )$
$d( , )$
$e( , )$

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: Find the coordinates of each vertex

• For point \(B(-1, - 10)\), after reflection over \(y=x\), using the rule \((x,y)\to(y,x)\), we get \(B'(-10,-1)\).
• For point \(C(-1,-1)\), after reflection over \(y = x\), using the rule \((x,y)\to(y,x)\), we get \(C'(-1,-1)\).
• For point \(D(8,-2)\), after reflection over \(y=x\), using the rule \((x,y)\to(y,x)\), we get \(D'(-2,8)\).
• For point \(E(8,-7)\), after reflection over \(y=x\), using the rule \((x,y)\to(y,x)\), we get \(E'(-7,8)\).

Answer:

\(B'(-10,-1)\), \(C'(-1,-1)\), \(D'(-2,8)\), \(E'(-7,8)\)