Question

apply the following transformations to the shape: first reflect over $x = 0$, then translate 5 units left and 4 units up. show your work here draw

Explanation:

Step1: Reflect over \(x = 0\) (y - axis)

The rule for reflection over the \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Translate 5 units left and 4 units up

The rule for translation 5 units left (\(x\) - coordinate: \(x-5\)) and 4 units up (\(y\) - coordinate: \(y + 4\)) is \((x,y)\to(x-5,y + 4)\).

Combining the two transformations:
If we start with a point \((x,y)\), after reflection over \(y\) - axis it is \((-x,y)\), and after translation it is \((-x-5,y + 4)\)

For example, if we take a blue - colored vertex at \((-2,3)\):

• After reflection over \(y\) - axis: \((2,3)\)
• After translation: \((2-5,3 + 4)=(-3,7)\)

Another blue - colored vertex at \((3,3)\):

• After reflection over \(y\) - axis: \((-3,3)\)
• After translation: \((-3-5,3 + 4)=(-8,7)\)

The blue - colored vertex at \((0,-3)\):

• After reflection over \(y\) - axis: \((0,-3)\)
• After translation: \((0-5,-3 + 4)=(-5,1)\)

Answer:

To draw the final shape, use the transformation rule \((x,y)\to(-x - 5,y + 4)\) for each vertex of the original blue - colored shape. Plot the new vertices \((-x-5,y + 4)\) and connect them to get the transformed shape.