Question
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
(9 5).
Determine the area of triangle ABC
Answers
Answered by
GPT 3.5
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.
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.
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