Question

a certain mapping in the xy-plane has the following properties:

• every point moves m units horizontally and n units vertically.
• if m is positive, the point moves to the right. if m is negative, the point moves to the left.
• if n is positive, the point moves up. if n is negative, the point moves down.

which transformation does the mapping define?
choose 1 answer:
a a translation
b a reflection
c a rotation

Explanation:

• A translation in the xy - plane is a transformation that moves every point of a figure or a point a fixed distance in a fixed direction (horizontal and vertical in this case). Here, each point moves m units horizontally and n units vertically, which matches the definition of a translation.
• A reflection is a transformation that flips a figure over a line (like the x - axis, y - axis, or another line), which is not what is happening here as there is no flipping over a line.
• A rotation is a transformation that turns a figure around a fixed point (like the origin) by a certain angle, which is also not the case here as there is no turning around a point.

Answer:

A. A translation