Question

the point (5, 3) has an image of (2, -1) under a translation of left 3 and down 4 units. which sequence of transformations produces the same image?
reflect over the x - axis, and then translate left 2 units and down 3 units.
reflect over the x - axis, and then translate left 3 units and down 2 units.
translate left 3 units and down 2 units, and then reflect over the x - axis.
translate left 2 units and down 3 units, and then reflect over the x - axis.

Explanation:

Step1: Analyze the first transformation

The original point is \((5,3)\). Translating left \(3\) units and down \(4\) units:
For \(x\)-coordinate: \(5 - 3=2\).
For \(y\)-coordinate: \(3-4=-1\). The image is \((2,-1)\).

Step2: Analyze the first option

Reflect \((5,3)\) over the \(x\)-axis: \((5,-3)\). Then translate left \(2\) units: \(5 - 2 = 3\), down \(3\) units: \(-3-3=-6\). The image is \((3,-6)
eq(2,-1)\).

Step3: Analyze the second option

Reflect \((5,3)\) over the \(x\)-axis: \((5,-3)\). Then translate left \(3\) units: \(5 - 3=2\), down \(2\) units: \(-3 - 2=-5\). The image is \((2,-5)
eq(2,-1)\).

Step4: Analyze the third option

Translate \((5,3)\) left \(3\) units: \(5 - 3 = 2\), down \(2\) units: \(3-2 = 1\). Then reflect over the \(x\)-axis: \((2,-1)\).

Step5: Analyze the fourth option

Translate \((5,3)\) left \(2\) units: \(5 - 2=3\), down \(3\) units: \(3 - 3=0\). Then reflect over the \(x\)-axis: \((3,0)
eq(2,-1)\).

Answer:

The third transformation (Translate left \(3\) units and down \(2\) units, and then reflect over the \(x\)-axis)