Question

given the graph of \\( \delta t u v \\), find the coordinates of the \\( \delta t ^ { \prime } u ^ { \prime } v ^ { \prime } \\).

• reflection about the \\( y \\)-axis, followed by \\( ( x, y ) \

ightarrow ( x + 4, y - 5 ) \\)
\\( t ^ { \prime } ( \square, \square ) \\)
\\( u ^ { \prime } ( \square, \square ) \\)
\\( v ^ { \prime } ( \square, \square ) \\)

Explanation:

Step1: Find original coordinates

From the graph, \(T(1,2)\), \(U(4,2)\), \(V(3, - 1)\)

Step2: Reflect about the \(y\) - axis

The rule for reflection about the \(y\) - axis is \((x,y)\to(-x,y)\).
For \(T(1,2)\), after reflection \(T'( - 1,2)\)
For \(U(4,2)\), after reflection \(U'( - 4,2)\)
For \(V(3,-1)\), after reflection \(V'( - 3,-1)\)

Step3: Translate using \((x,y)\to(x + 4,y-5)\)

For \(T'(-1,2)\): \(x=-1+4 = 3\), \(y=2 - 5=-3\), so \(T''(3,-3)\)
For \(U'(-4,2)\): \(x=-4 + 4=0\), \(y=2-5=-3\), so \(U''(0,-3)\)
For \(V'(-3,-1)\): \(x=-3 + 4 = 1\), \(y=-1-5=-6\), so \(V''(1,-6)\)

Answer:

\(T''(3,-3)\), \(U''(0,-3)\), \(V''(1,-6)\)