Question

Triangle abc will undergo two transformations will give triangle a’b’c’. Which pair you f transformation will give a different image of triangle abc if the order of the transformations is reversed?

A- a rotation 90 degrees counterclockwise about the origin followed by a reflection across the y-axis
B- a translation 5 units down followed by a translation 4 units to the right
C- a reflection across the x-axis followed by a reflection across the y-axis
D- a rotation 180 degrees clockwise about the origin followed a reflection across the y-axis

Answer 1

A. a rotation 90° counterclockwise about the origin followed by a reflection across the y-axis

Explanation:

Answer 2

The correct answer is:

A) A 90° counterclockwise rotation about the origin followed by a reflection across the y-axis.

Explanation:

We will represent the transformations algebraically.

For A:
A 90° rotation counterclockwise maps
(x,y)→(-y,x).

A reflection across the y-axis negates the x-coordinate; this maps our new point
(-y,x)→(y,x).

If we reverse these and reflect across the y-axis first, negating the x-coordinate, we map
(x,y)→(-x,y).

Rotating this 90° counterclockwise, we reverse the x- and y-coordinates and negate the new x:
(-x,y)→(-y,-x).

Since these are different end coordinates, this is the correct answer.