Triangle M was dilated by a scale factor of 1.2 to form triangle M. How does the area of triangle M' relate to the area of triangle M?
A- The area of triangle M'is 0.6 times the area of triangle M.
B- The area of triangle M'is 1.2 times the area of triangle M.
C- The area of triangle M'is 1.44 times the area of triangle M.
D- The area of triangle M' is 2.4 times than the area of triangle M.

The area of triangle M is 1.44 times the area of triangle M.

Step-by-step explanation:

From Geometry we remember that the area formula of the triangle is:

(1)

Where:

- Base of the triangle, dimensionless.

- Height of the triangle, dimensionless.

- Area of the triangle, dimensionless.

The dillation of the triangle by a scale factor means that:

(2)

(3)

(4)

Where:

- Dilated base of the triangle, dimensionless.

- Dilated height of the triangle, dimensionless.

- Dilated area of the triangle, dimensionless.

- Dilation factor, dimensionless.

If we know that , then the area formula for the dilated triangle is:

Therefore, the area of triangle M is 1.44 times the area of triangle M.

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