Question

Triangle ABC with an area of 15cm3 is mapped onto triangle A'B'C' using matrix M=(2 -3)
(1 1).Find the area of the triangle A'B'C'

Answer 1

To find the area of triangle A'B'C', we can use the formula for the area of a triangle given its vertices. However, since the matrix M represents a linear transformation, the area of the triangle A'B'C' will be scaled by the determinant of the matrix.

The given matrix is M = (2 -3)
(1 1)

The determinant of M is det(M) = (2*1) - (-3*1) = 2 + 3 = 5.

The area of triangle A'B'C' can be calculated as follows:

Area(A'B'C') = det(M) * Area(ABC)
= 5 * 15 cm^2
= 75 cm^2

Therefore, the area of triangle A'B'C' is 75 cm^2.