Question

Triangle ABC is drawn in a coordinate plane. Triangle ABC is reflected over the line y = 3 and triangle A'B'C' is reflected over the line x = −2.

Draw a coordinate grid with the x and y axes labeled and draw triangle ABC with point A at (3, −3), point B at (5, −5), and point C at (8, −2).
Draw the image of triangle ABC reflected over the line y = 3, and label this image A'B'C'. Draw the image of triangle A'B'C' reflected over the line x = −2. Label this image A''B''C''.
Explain your work on the "Triangle ABC Reflected" handout.

Answer 1

To reflect triangle ABC over the line y = 3, subtract the y-coordinate of each point from the equation of the line. To reflect triangle A'B'C' over the line x = -2, subtract the x-coordinate of each point from the equation of the line.

Step-by-step explanation:

To draw the image of triangle ABC reflected over the line y = 3, we need to reflect each point of triangle ABC over the line y = 3. To do this, we need to find the new y-coordinate by subtracting the y-coordinate of the original point from the equation of the line. For example, the y-coordinate of point A is -3, so the new y-coordinate is 3 - (-3) = 6. The new coordinates for point A' are (3,6).

To draw the image of triangle A'B'C' reflected over the line x = -2, we need to reflect each point of triangle A'B'C' over the line x = -2. To do this, we need to find the new x-coordinate by subtracting the x-coordinate of the original point from the equation of the line. For example, the x-coordinate of point A' is 3, so the new x-coordinate is -2 - 3 = -5. The new coordinates for point A'' are (-5,6).