Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C'. Describe the transformation using words. Make sure you refer to the characteristics and the coordinates. Draw a line segment from point A to the reflecting line, and then draw a line segment from point A' to the reflecting line. What do you notice about the two line segments you drew? Do you think you would see the same characteristic if you drew the line segment connecting B with the reflecting line and then B' with the reflecting line? How do you know?

Part A

We note that the vertices of a triangle are formed by three non colinear points, which are A(3, 3), B(6, 6), C(9, 3)

The image of the reflection of a point (x, y) across the x-axis is (x, -y)

Therefore, the image of the triangle are; A'(3, -3), B'(6, -6), and C'(9, -3)

The characteristics of the transformation includes;

1) The dimensions of the preimage and image triangles are the same (rigid transformation)

2) The image is the representation of the inverted (upside down) of the  preimage

3) The x-values of the image and the preimage are the same, while the y values are equal in magnitude but opposite in sign

Part B

Please find attached the drawing of the triangle ΔABC, ΔA'B'C' and the lines from A and and A' to the reflecting line, the x-axis

Based on the above characteristics, the perpendicular line drawn from A to the reflecting line(the x-axis and the line drawn from A' to the x-axis are equal in length and they intersect at the same point on the x-axis

Part C

Given that the x-axis values of B and B' and the magnitudes of the y-axis values of B and B' are the same, we have that the length of the perpendicular lines from B and B' will have equal length and point of intersection on the x-axis

Therefore, the same characteristics is seen when a line segment connecting B with the reflecting x-axis and then a line B' with the reflecting line is drawn

Step-by-step explanation: