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Answer:
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:
