Triangle ABC with an area of 15cm³is mapped onto triangle A'B'C'using matrix M=(2 -3)
(1 1)
Find the area of the triangle A'B'C'
To find the area of triangle A'B'C', we can use the formula for the area of a triangle:
Area (A'B'C') = |det(M)| * Area (ABC)
First, let's find the determinant of matrix M:
det(M) = (2 * 1) - (-3 * 1) = 5
Now, we can calculate the area of triangle A'B'C':
Area (A'B'C') = |5| * 15
= 5 * 15
= 75 cm³
Therefore, the area of triangle A'B'C' is 75 cm³.
To find the area of triangle A'B'C', we need to use the transformation matrix M and apply it to the area of triangle ABC.
Given that the matrix M = (2 -3)
(1 1)
We can calculate the new area of triangle A'B'C' by multiplying the area of triangle ABC by the determinant of matrix M.
The determinant of matrix M is: (2 * 1) - (-3 * 1) = 2 + 3 = 5
Therefore, the area of triangle A'B'C' is (area of triangle ABC) * (determinant of matrix M) = 15 * 5 = 75 cm³.