Question

Which of the following transformations could map point C(2,4) to F(4,-2)?

A) Translation 2 units to the right and 6 units down.
B) Rotation of 180 degrees about the origin (0,0).
C) Reflection over the y-axis.
D) Dilation with a scale factor of 2.

Answer 1

A translation 2 units to the right and 6 units down would map point C(2,4) to F(4,-2). This involves adding 2 to the x-coordinate and subtracting 6 from the y-coordinate. The other options either change the sign or magnitude of the coordinates differently.

Step-by-step explanation:

The transformation that could map point C(2,4) to F(4,-2) is Translation 2 units to the right and 6 units down. This can be seen as a two-step process:

• Translation horizontally to the right side of the coordinate system (c): This means you would add 2 to the x-coordinate of point C, changing it from (2, 4) to (4, 4).
• Translation vertically downward in the coordinate system (b): This entails subtracting 6 from the y-coordinate of the new position of point C, changing it from (4, 4) to (4, -2), which matches point F.

The other transformations have different effects:

• A rotation of 180 degrees about the origin would map point C to (-2, -4), not to F(4, -2).
• A reflection over the y-axis would map point C to (-2, 4), again not to F(4, -2).
• A dilation with a scale factor of 2 would map point C to (4, 8), not to F(4, -2).