Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A scientist is studying the movement of a particle on a coordinate plane. The particle starts at (3, 2) and undergoes a dilation centered at the origin with a scale factor of 3. What are the new coordinates of the particle after this transformation?
- A(3, 2)
- B(18, 12)
- C(9, 6)
- D(6, 9)
Show answer & explanationAnswer & explanation
Correct answer: C. (9, 6)
A dilation centered at the origin with a scale factor 'k' transforms a point (x, y) to (kx, ky). In this case, the scale factor is 3, so multiply both the x and y coordinates by 3.
Why the other options are wrong
- A. This is incorrect; it shows no transformation occurred.
- B. This is incorrect; it might be the result of applying the scale factor twice or an incorrect calculation.
- D. This is incorrect; the coordinates are swapped and scaled incorrectly.
Dilation (Centered at Origin)
A transformation that changes the size of a figure by a specific scale factor, with the origin as the center of dilation.
- Each coordinate (x, y) is multiplied by the scale factor 'k'.
- Transformed point becomes (kx, ky).
- If k > 1, the figure gets larger; if 0 < k < 1, it gets smaller.
Memory trick: Dilation from Origin: 'Scale' up 'X' and 'Y' equally!