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Scale triangle Sx=3, Sy=2

Short answer

Multiply each vertex by scaling factors: x' = 3x, y' = 2y. A(18,18), B(30,10), C(12,6).

Perform scaling transformation to the triangle with vertices A (6, 9), B (10, 5), C (4, 3) with scaling factors Sx = 3 and Sy = 2. [Show the necessary transformation matrix]

Scaling about the origin multiplies each coordinate: x' = Sx·x, y' = Sy·y.

Scaling matrix (homogeneous): with Sx = 3, Sy = 2

S = | 3 0 0 |
    | 0 2 0 |
    | 0 0 1 |

The vertices as columns of the matrix P, and P' = S · P:

      A   B   C                  A'  B'  C'
P = |  6  10   4 |        P' = | 18  30  12 |
    |  9   5   3 |             | 18  10   6 |
    |  1   1   1 |             |  1   1   1 |

Step by step:

A(6,9):   x' = 3×6  = 18,   y' = 2×9 = 18
B(10,5):  x' = 3×10 = 30,   y' = 2×5 = 10
C(4,3):   x' = 3×4  = 12,   y' = 2×3 = 6

Answer: A'(18, 18), B'(30, 10), C'(12, 6). The triangle is enlarged 3 times in x and 2 times in y, and since scaling is about the origin, it also moves away from the origin.

✓ Answer checked by Claude Opus 5.5 (high effort)

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