Question

graph the image of \\( \triangle xyz \\) after the following sequence of transformations:
reflection across the \\( x \\)-axis
translation 18 units right and 17 units up

Explanation:

Step1: Find the coordinates of \(\triangle XYZ\)

Assume \(X(-6,13)\), \(Y(-12,9)\), \(Z(-8,3)\)

Step2: Reflect across the \(x -\)axis

The rule for reflection across the \(x -\)axis is \((x,y)\to(x, - y)\)
For \(X(-6,13)\), after reflection \(X_1(-6,-13)\)
For \(Y(-12,9)\), after reflection \(Y_1(-12,-9)\)
For \(Z(-8,3)\), after reflection \(Z_1(-8,-3)\)

Step3: Translate 18 units right and 17 units up

The rule for translation is \((x,y)\to(x + 18,y+17)\)
For \(X_1(-6,-13)\): \(x=-6 + 18=12\), \(y=-13 + 17 = 4\), so \(X_2(12,4)\)
For \(Y_1(-12,-9)\): \(x=-12+18 = 6\), \(y=-9 + 17=8\), so \(Y_2(6,8)\)
For \(Z_1(-8,-3)\): \(x=-8 + 18=10\), \(y=-3+17 = 14\), so \(Z_2(10,14)\)

Plot the points \(X_2(12,4)\), \(Y_2(6,8)\), \(Z_2(10,14)\) and connect them to get the image of \(\triangle XYZ\) after the given sequence of transformations.

Answer:

Plot the points \((12,4)\), \((6,8)\) and \((10,14)\) and connect them.