Question

in 1 - 2 sentences, identify what composition transformation maps $delta abc\todelta abc$. (2 points)

Explanation:

Step1: Determine the translation

First, observe the horizontal movement. The \(x\)-coordinate of each point in \(\triangle ABC\) increases by \(10\) (e.g., \(A(-5,4)\) to \(A''(6,0)\), \(-5 + 10=5\) (wait, no, better: for \(A(-5,4)\) to \(A''(6,0)\), the \(x\)-translation: \(6-(-5)=11\), \(y\)-translation: \(0 - 4=-4\). But another way: consider the vector. Or note that \(\triangle ABC\) is first reflected over the \(x\)-axis (changes \(y\)-coordinate sign: \((x,y)\to(x, - y)\)) and then translated.
For a point \(P(x,y)\) in \(\triangle ABC\), after reflection over the \(x\)-axis \(P'(x,-y)\), then translated \((x + 10,y- 4)\) (incorrect approach. Correct:
Let's take \(A(-5,4)\), \(B(-2,2)\), \(C(-1,5)\)
After reflection over \(x\)-axis: \(A'(-5,-4)\), \(B'(-2,-2)\), \(C'(-1,-5)\)
Then translated \(11\) units to the right (add \(11\) to \(x\)-coordinate) and \(4\) units up (add \(4\) to \(y\)-coordinate)
\(A'(-5,-4)\to A''(6,0)\), \(B'(-2,-2)\to B''(9,2)\) (no, wait, looking at the graph:
Another approach:
The transformation is a reflection over the \(x\)-axis (flips the triangle vertically) followed by a translation \(10\) units to the right (adds \(10\) to the \(x\)-coordinate of each point)

Answer:

The composition transformation is a reflection over the \(x\)-axis followed by a translation \(10\) units to the right.