Question

graph the image of \\( \triangle vwx \\) after the following sequence of transformations: reflection across the y - axis translation 2 units right and 13 units up

Explanation:

Step1: Find the coordinates of the original triangle

Assume the coordinates of \( V\), \( W\), \( X\) are \( V(-11,-9)\), \( W(-7,-5)\), \( X(-3,-9)\)

Step2: Reflection across the \( y\) - axis

The rule for reflection across the \( y\) - axis is \((x,y)\to(-x,y)\)
For \( V(-11,-9)\), after reflection \( V_1(11,-9)\)
For \( W(-7,-5)\), after reflection \( W_1(7,-5)\)
For \( X(-3,-9)\), after reflection \( X_1(3,-9)\)

Step3: Translation 2 units right and 13 units up

The rule for translation is \((x,y)\to(x + 2,y+13)\)
For \( V_1(11,-9)\), after translation \( V_2(11 + 2,-9+13)=(13,4)\)
For \( W_1(7,-5)\), after translation \( W_2(7 + 2,-5+13)=(9,8)\)
For \( X_1(3,-9)\), after translation \( X_2(3 + 2,-9+13)=(5,4)\)

Step4: Plot the new points

Plot the points \( (13,4)\), \( (9,8)\), \( (5,4)\) and connect them to form the image of \(\triangle VWX\)

Answer:

Plot the points \( (13,4)\), \( (9,8)\), \( (5,4)\) and connect them.