Question

question 6 of 10

if \\(abcde\\) is translated 2 units to the right and 4 units up, what will happen to the polygon?

a. it will stay where it is but get bigger.
b. it will move but wont change shape or size.
c. it will move and change shape.
d. it will move, change shape, and change size.

Explanation:

Define translation properties

$$ T_{(x, y)} \to (x + 2, y + 4) $$

Analyze effect on shape and size

$$ \text{Translation} \implies \text{Rigid Transformation} \implies \text{Isometry} $$

$$ \text{Distance}(P, Q) = \text{Distance}(T(P), T(Q)) $$

Match with options

$$ \text{Movement} = \text{Yes},\quad \text{Shape Change} = \text{No},\quad \text{Size Change} = \text{No} $$

Answer:

• A. It will stay where it is but get bigger.
• B. It will move but won't change shape or size. (Correct answer)
• C. It will move and change shape.
• D. It will move, change shape, and change size.