Question

this is level 1; reflect a shape in a given line. click on coordinates to draw your image.
draw the reflection of the shape in the y axis.
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draw the reflection of the shape in the y axis.
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Explanation:

First Sub - Question (Reflecting the Green Shape over the y - axis)

Step 1: Identify Key Points

For a reflection over the \(y\) - axis, the rule is \((x,y)\to(-x,y)\). First, find the coordinates of the vertices of the green shape. Let's assume the grid has a side length of 1 unit. The green shape has vertices (let's take the bottom - left corner of the main rectangle part as a reference). Suppose the original green shape has vertices with \(x\) - coordinates positive (since it's on the right side of the \(y\) - axis). For example, if a vertex is at \((x,y)\), after reflection over the \(y\) - axis, it will be at \((-x,y)\).

Step 2: Plot Reflected Points

Take each vertex of the green shape, apply the reflection rule \((x,y)\to(-x,y)\), and then plot these new points on the left - hand side of the \(y\) - axis (since the original is on the right). Connect the points in the same order as the original shape to get the reflected image.

Second Sub - Question (Reflecting the Blue Shape over the y - axis)

Step 1: Identify Key Points

For the blue shape, which is on the left side of the \(y\) - axis (with \(x\) - coordinates negative), use the reflection rule over the \(y\) - axis \((x,y)\to(-x,y)\). So, if a vertex has coordinates \((x,y)\) where \(x\lt0\), the reflected vertex will have coordinates \((-x,y)\) (which will be on the right side of the \(y\) - axis).

Step 2: Plot Reflected Points

Take each vertex of the blue shape, apply the reflection rule, and plot the new points on the right - hand side of the \(y\) - axis. Connect the points in the same order as the original blue shape to form the reflected image.

Answer:

For the green shape: The reflected shape will be a mirror image of the green shape across the \(y\) - axis, with all \(x\) - coordinates of the vertices negated (while \(y\) - coordinates remain the same).
For the blue shape: The reflected shape will be a mirror image of the blue shape across the \(y\) - axis, with all \(x\) - coordinates of the vertices negated (while \(y\) - coordinates remain the same). To draw them, plot the reflected vertices and connect them as per the original shape's outline.