Question

write the coordinates of the vertices after a reflection over the line $y = x$.
$q(\square,\square)$
$r(\square,\square)$
$s(\square,\square)$
$t(\square,\square)$

Explanation:

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

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

Step2: Find the coordinates of the original points

From the graph:

• \(Q(- 4,-10)\)
• \(R(-4,-4)\)
• \(S(0,-4)\)
• \(T(0,-10)\)

Step3: Apply the reflection rule

• For \(Q(-4,-10)\): Using the rule \((x,y)\to(y,x)\), we get \(Q'(-10,-4)\)
• For \(R(-4,-4)\): Using the rule \((x,y)\to(y,x)\), we get \(R'(-4,-4)\)
• For \(S(0,-4)\): Using the rule \((x,y)\to(y,x)\), we get \(S'(-4,0)\)
• For \(T(0,-10)\): Using the rule \((x,y)\to(y,x)\), we get \(T'(-10,0)\)

Answer:

\(Q'(-10,-4)\)
\(R'(-4,-4)\)
\(S'(-4,0)\)
\(T'(-10,0)\)