Question

graph the image of \\( \triangle a b c \\) after the following sequence of transformations:

rotation \\( 90^{circ} \\) counterclockwise around the origin

reflection across the \\( x \\)-axis

Explanation:

Step1: Find coordinates of \(A\), \(B\), \(C\)

From the graph, \(A(-11,-6)\), \(B(-3,-3)\), \(C(-11,3)\)

Step2: Apply rotation \(90^{\circ}\) counter - clockwise around the origin

The rule for a \(90^{\circ}\) counter - clockwise rotation around the origin \((x,y)\to(-y,x)\)

• For \(A(-11,-6)\): \((-(-6),-11)=(6,-11)\)
• For \(B(-3,-3)\): \((-(-3),-3)=(3,-3)\)
• For \(C(-11,3)\): \((-3,-11)\)

Step3: Apply reflection across the \(x\) - axis

The rule for reflection across the \(x\) - axis \((x,y)\to(x,-y)\)

• For the rotated point \(A'(6,-11)\): \((6,11)\)
• For the rotated point \(B'(3,-3)\): \((3,3)\)
• For the rotated point \(C'(-3,-11)\): \((-3,11)\)

Answer:

Plot the points \((6,11)\), \((3,3)\), \((-3,11)\) and connect them to form the image of \(\triangle ABC\) after the given sequence of transformations.