Question

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Answer 1

Following transformations on Triangle ABC will result in the Triangle A'B'C'

a) Reflection the triangle across x-axis
b) Shift towards Right by 2 units
c) Shift upwards by 6 units

In Triangle ABC, the coordinates of the vertices are:
A (1,9)
B (3, 12)
C (4, 4)

In Triangle A'B'C, the coordinates of the vertices are:
A' (3, -3)
B' (5, -6)
C' (6, 2)

First consider point A of Triangle ABC.
Coordinate of A are (1, 9). If we reflect it across x-axis the coordinate of new point will be (1, -9). Moving it 2 units to right will result in the point (3, -9). Moving it 6 units up will result in the point (3,-3) which are the coordinates of point A'. 

Coordinates of B are (3,12). Reflecting it across x-axis, we get the new point (3, -12). Moving 2 units towards right, the point is translated to (5, -12). Moving 6 units up we get the point (5, -6), which are the coordinate of B'. 

The same way C is translated to C'.

Thus the set of transformations applied on ABC to get A'B'C' are:
a) Reflection the triangle across x-axis
b) Shift towards Right by 2 units
c) Shift upwards by 6 units