Triangle ABC with an area of 15cm³is mapped onto triangle A'B'C'using matrix M=(2 -3)

Question

(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:

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.