Question

reflections practice problems
reflect the figure across the y - axis.
vertices of preimage vertices of image
reflect the figure across the x - axis.
vertices of preimage vertices of image
reflect the figure across the line y = x
vertices of preimage vertices of image
reflect the figure across the x - axis.
vertices of preimage vertices of image

Explanation:

Step1: Recall reflection rules

• Reflection across y - axis: $(x,y)\to(-x,y)$.
• Reflection across x - axis: $(x,y)\to(x, - y)$.
• Reflection across $y = x$: $(x,y)\to(y,x)$.

Step2: For first problem (reflect across y - axis)

Identify pre - image vertices, say $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. New vertices are $(-x_1,y_1),(-x_2,y_2),(-x_3,y_3)$.

Step3: For second problem (reflect across x - axis)

If pre - image vertices are $(x_4,y_4),(x_5,y_5),(x_6,y_6),(x_7,y_7)$ (for rectangle), new vertices are $(x_4,-y_4),(x_5,-y_5),(x_6,-y_6),(x_7,-y_7)$.

Step4: For third problem (reflect across $y = x$)

If pre - image vertices are $(x_8,y_8),(x_9,y_9),(x_{10},y_{10}),(x_{11},y_{11})$ (for trapezoid), new vertices are $(y_8,x_8),(y_9,x_9),(y_{10},x_{10}),(y_{11},x_{11})$.

Step5: For fourth problem (reflect across x - axis)

If pre - image vertices are $(x_{12},y_{12}),(x_{13},y_{13}),(x_{14},y_{14}),(x_{15},y_{15})$ (for rhombus), new vertices are $(x_{12},-y_{12}),(x_{13},-y_{13}),(x_{14},-y_{14}),(x_{15},-y_{15})$.

Since we don't have actual vertex coordinates from the image, we can't give specific numerical answers. But the general method for finding the vertices of the image after reflection is as described above.

Answer:

The general rules for finding vertices of the reflected image are:

• Across y - axis: $(x,y)\to(-x,y)$.
• Across x - axis: $(x,y)\to(x, - y)$.
• Across $y = x$: $(x,y)\to(y,x)$.

Actual coordinates of image vertices depend on pre - image vertex coordinates which are not provided in a numerical form in the given image.