The statements about the reflection and translation of the line segments that are true include;
B. The coordinates of point C' in the final image are (1,4).
E. When reflected over the x-axis, the coordinates of point A become (2,-4).
G. The final image will result in parallel segments slanted in the opposite direction and the same distance apart as the pre-image segments.
In Mathematics and Geometry, a reflection over the x-axis is represented by this transformation rule (x, y) → (x, -y). By applying a reflection across the x-axis to the coordinates of segments AB and CD, we have;
(x, y) → (x', -y')
A (2, 4) → A' (2, -4)
B (-2, -1) → B' (-2, 1)
C (3, 1) → C' (3, -1)
D (-1, -4) → D' (-1, 4)
Next, we would translate the new segments 2 units left and 5 units up;
(x, y) → (x - 2, y + 5)
A' (2, -4) → A' (0, 1)
B' (-2, 1) → B' (-4, 6)
C' (3, -1) → C' (1, 4)
D (-1, 4) → D' (-3, 9)
Missing information:
Giselle starts with the two parallel line segments shown. She correctly reflects the segments across the x-axis and then translates them following the rule (x,y) → (x-2,y+5). Line Segment AB has endpoints (2,4) and (-2,-1). Line Segment CD has end points (3,1) and (-1,-4).
Which statements about the reflection and translation of the line segments are true? Select all that apply.
The final image will result in parallel segments slanted in the same direction and closer together than the pre-image segments.
The coordinates of point C' in the final image are (1,4).
The coordinates of point B' in the final image are (0,6).
The final image will result in perpendicular segments that intersect at point (0,1).
When reflected over the x-axis, the coordinates of point A become (2,-4)
When reflected over the x-axis, the coordinates of point D become (1,-4).
The final image will result in parallel segments slanted in the opposite direction and the same distance apart as the pre-image segments.