Identify the scale factor used to map Triangle A(2,3), B(1,6), C(0,4) onto Triangle D(3,4.5), E(1.5,9), F(0,6).

The scale factor used to map Triangle A onto Triangle D is determined by calculating the ratios of the distances between corresponding points of the triangles and simplifying the result, which is approximately 1.43.

Explanation:

To identify the scale factor used to map Triangle A(2,3), B(1,6), C(0,4) onto Triangle D(3,4.5), E(1.5,9), F(0, 6), we need to compare the corresponding sides of the triangles. Let's take the distance between points A and B in Triangle A and points D and E in Triangle D as an example.

First, calculate the distance AB using the distance formula √((x2 - x1)^2 + (y2 - y1)^2). So AB = √((1 - 2)^2 + (6 - 3)^2) = √(1 + 9) = √10.
Next, calculate the distance DE using the same formula. DE = √((1.5 - 3)^2 + (9 - 4.5)^2) = √(2.25 + 20.25) = √22.5.
To find the scale factor, we then form a ratio of DE to AB. This gives us √22.5 / √10 = 4.5 / 3.15.
Simplify the fraction to determine the scale factor, which is approximately 1.43 or 1.5/1.05 when expressed in a more simplified form.

Therefore, the scale factor used to map the original triangle onto the new triangle is approximately 1.43.