The graph of the triangle with vertices L(1, 6), M(-2, 4), and N(3, 2), and the image of the triangle with vertices L''(3, 1), M''(1, 4), and N(-1, -1), created using MS Excel is attached
The steps used to find the graph of the triangle and the image of the triangle can be presented as follows;
The coordinates of the point (x, y) following a 90° clockwise rotation about the origin is the point (y, -x)
Therefore, the coordinates of the vertices of the image of the triangle ΔLMN after a rotation 90° about the origin are;
L(1, 6) ⇒ 90° rotation about the origin ⇒ L'(6, -1)
M(-2, 4) ⇒ 90° rotation about the origin ⇒ M'(4, 2)
N(3, 2) ⇒ 90° rotation about the origin ⇒ N'(2, -3)
The translation transformation can be applied to the coordinates of the vertices of the image of the triangle ΔLMN, to get;
L'(6, -1) → (x - 3, y + 2) → L''(3, 1)
M'(4, 2) → (x - 3, y + 2) → M''(1, 4)
N'(2, -3) → (x - 3, y + 2) → N''(, -1, -1)
Please find attached the graph of the triangle ΔLMN and its image, created using MS Excel