ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line

Question

3 years ago

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ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line

y = -x. What are the coordinates of the vertices of the image?
A(. A'(0, 3), B'(2, 3), C'(1, 1)
B(. A'(0, -3), B'(3, -2), C'(1, -1)
C(. A'(-3, 0), B'(-3, 2), C'(-1, 1)
D(. A'(0, -3), B'(-2, -3), C'(-1, -1)

Mathematics

1 answer:

Flauer [41] · Answer 1 · 2022-05-08T16:17:38+03:00

Answer: B

Picture 1 shows the reflection of ABC 180° clockwise about the origin. To draw A'B'C' we draw the line segments AO, BO, and CO and extend them such that O is the midpoint of line segments AA', BB', and CC' respectively.

Picture 2 shows the line y=-x (the yellow line.) This is the line containing all points of the form (x, -x), that is, this points contains (1, -1), (-2, 2) etc...

We see that point C' is already on this line, and we draw the reflections of points B and C with respect to this line, to find B'' and C'' with coordinates as shown in the figure.