Question

type in the correct ordered pairs after the transformation given. complete a reflection over y=-3, a ( , ) b ( , ) c ( , )

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points A, B, C. From the graph:

• A: Let's assume A is at \((-1, 0)\) (since it's on the x - axis, left of y - axis)
• B: Let's assume B is at \((4, 2)\) (by counting grid squares)
• C: Let's assume C is at \((5, -2)\) (by counting grid squares)

Step2: Reflection formula over \(y = k\)

The formula for reflecting a point \((x,y)\) over the line \(y=k\) is \((x, 2k - y)\). Here, \(k=-3\), so the formula becomes \((x,2(-3)-y)=(x, - 6 - y)\)

Step3: Reflect point A

For A \((-1,0)\):
Using the formula \(x=-1\), \(y = 0\)
New \(y\) - coordinate: \(-6-0=-6\)
So \(A'=(-1,-6)\)

Step4: Reflect point B

For B \((4,2)\):
\(x = 4\), \(y = 2\)
New \(y\) - coordinate: \(-6 - 2=-8\)
So \(B'=(4,-8)\)

Step5: Reflect point C

For C \((5,-2)\):
\(x = 5\), \(y=-2\)
New \(y\) - coordinate: \(-6-(-2)=-6 + 2=-4\)
So \(C'=(5,-4)\)

Answer:

\(A'(-1,-6)\), \(B'(4,-8)\), \(C'(5,-4)\)