Question

triangle abc and triangle abc are shown on the right. a student says that they can reflect triangle abc across the x - axis and then translate it 10 units to the right in order to create abc. do you agree with this student? justify your reasoning in the space below.

Explanation:

Step1: Find coordinates of original triangle

Assume \(A(-6,7)\), \(B(-8,2)\), \(C(-4,2)\)

Step2: Reflect across x - axis

The rule for reflection across \(x\) - axis is \((x,y)\to(x, - y)\). So \(A_1(-6,-7)\), \(B_1(-8,-2)\), \(C_1(-4,-2)\)

Step3: Translate 10 units right

The rule for translation \(10\) units right is \((x,y)\to(x + 10,y)\). So \(A'(-6+10,-7)=(4,-7)\), \(B'(-8 + 10,-2)=(2,-2)\), \(C'(-4+10,-2)=(6,-2)\)

Step4: Check with the graph

From the graph, \(A'(4,-7)\), \(B'(2,-2)\), \(C'(6,-2)\) which matches the coordinates obtained from the transformation

Answer:

Yes, the student is correct.