Question

graph the image of the figure using the transformation given. 9) reflection across y = 2 10) reflection across the y - axis 11) reflection across x=-2 12) reflection across the x - axis

Explanation:

Step1: Recall reflection rules

For reflection across $y = c$, the rule for a point $(x,y)$ is $(x,2c - y)$. For reflection across $x = d$, the rule is $(2d - x,y)$. For reflection across the $y$-axis, the rule is $(-x,y)$ and for reflection across the $x$-axis, the rule is $(x,-y)$.

Step2: For reflection across $y = 2$

Let's assume a point $(x,y)$ on the original figure. The new - point after reflection across $y = 2$ is $(x,4 - y)$. Identify the vertices of the original triangle, apply the rule to each vertex, and then connect the new vertices to get the reflected image.

Step3: For reflection across the $y$-axis

If a vertex of the original triangle is $(x,y)$, its image after reflection across the $y$-axis is $(-x,y)$. Find the new coordinates of all vertices and graph the new triangle.

Step4: For reflection across $x=-2$

For a point $(x,y)$ on the original figure, the new point after reflection across $x = - 2$ is $(-4 - x,y)$. Determine the coordinates of the vertices of the original triangle, apply the rule, and draw the reflected triangle.

Step5: For reflection across the $x$-axis

If a vertex of the original triangle is $(x,y)$, its image after reflection across the $x$-axis is $(x,-y)$. Calculate the new coordinates of all vertices and plot the reflected triangle.

Since this is a graph - based problem and the actual graphing cannot be done in text, the general steps for finding the reflected points are provided above. To actually graph the images, one would need to use graph paper or a graphing utility and plot the points obtained from the above - mentioned rules.

Answer:

Follow the above - mentioned steps to graph the reflected images for each transformation.