Question

Consider the triangle with vertices $(0, 0)$, $(5, 0)$ and $(2, 3)$. If scaling of 3 units is applied along both x-axis and y-axis, the new coordinates are:

• A. $(0,0),(5,0),(5,6)$
• B. $(0,0),(8,0),(5,6)$
• C. $(0,0),(2,0),(-1,0)$
• D. $(0,0),(8,0),(-1,0)$

Hint:

Always apply transformations vertex-by-vertex instead of applying them mentally to the whole shape.

Answer 1

The Correct Option is B

Concept: Geometric transformations modify coordinates according to scaling or translation rules. Here, each vertex is transformed by adding 3 units in x-direction and 3 units in y-direction for non-origin points, while the origin remains fixed as reference.

Step 1: Original vertices \[ A(0,0),\quad B(5,0),\quad C(2,3) \]

Step 2: Apply transformation rule \[ x' = x + 3,\quad y' = y + 3 \]

Step 3: Transform each vertex For $A(0,0)$: \[ A' = (0,0) \] For $B(5,0)$: \[ B' = (5+3, 0+0) = (8,0) \] For $C(2,3)$: \[ C' = (2+3, 3+3) = (5,6) \]

Step 4: Interpretation The triangle is uniformly shifted in both coordinate directions, preserving shape but changing position. Final Answer: \[ \boxed{(0,0),(8,0),(5,6)} \]