Triangle A'B'C'is the image triangle ABC under a transformation represented by the matrix M=(3 2).If the area of the triangle A'B'C' is
(9 5).
Determine the area of triangle ABC
To determine the area of triangle ABC, we need to find the determinant of the matrix M.
Given that M = (3 2), the determinant is calculated as follows:
det(M) = (3 * 5) - (2 * 9) = 15 - 18 = -3
Since the determinant is negative, we need to take the absolute value.
|det(M)| = |-3| = 3
Therefore, the area of triangle ABC is 3.
To determine the area of triangle ABC, we need to find the determinant of the matrix M=(3 2) and multiply it by the area of triangle A'B'C'.
The matrix M represents a linear transformation, and the determinant of M gives us the scaling factor of the transformation. In this case, the determinant of M is 3.
Therefore, to find the area of triangle ABC, we multiply the determinant of M (3) by the area of triangle A'B'C' (9):
Area of triangle ABC = Determinant of M * Area of triangle A'B'C'
= 3 * 9
= 27
So, the area of triangle ABC is 27.