Question

What scale factor will dilate triangle ABC so that it has the same vertices as triangle DEF? Option 1: 0.25 Option 2: 0.5 Option 3: 1 Option 4: 2

Answer 1

When two triangles have the same vertices, their scale factor is 1. Scale factors are calculated by setting up proportions between the scale measurement and the actual measurement. The correct application of these proportions allows for accurate scaling of dimensions between models and their real-life counterparts.

Step-by-step explanation:

Understanding Scale Factors

When two triangles have the same vertices, their scale factor is 1, meaning they are congruent and have the same size and shape. For example, if a model's scale dimension is 4, and we want to find the actual dimension using the proportion 1:2 = 4:x, we cross-multiply to find that x equals 8. Now, if we have a scale factor where the scale measurement is smaller than the actual measurement, we can set up a proportion to find the missing dimension. For instance, if the scale factor is 1 cm = 0.5 m and the scale measurement is 0.25 m, we can use the proportion 1 cm : 0.5 m = x cm : 0.25 m to find that the actual measurement in centimeters is 0.5.

To determine scale factors for various situations, divide the scale measurement by the actual measurement. For example, to solve the proportion 1/4":4' = x:12' to find x, we multiply 12' by 1/4" and convert feet to inches if necessary, resulting in the actual dimension as x inches. Similarly, to find the length of a flower bed in a drawing using a scale factor of 1/20, we divide the actual length by 20. These examples demonstrate how to calculate and utilize scale factors in real situations.

Answer 2

A scale factor that will dilate triangle ABC so that it has the same vertices as triangle DEF is: Option 2: 0.5.

In Mathematics and Geometry, a scale factor can be calculated through the division of the side length of the image by the side length of the original or actual geometric figure (pre-image).

Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:

Scale factor = side length of image/side length of pre-image

Note: Each interval on the x-axis represents 1 unit.

In this context, the length of segment AE can be calculated as follows;

Scale factor = DE/AB

Scale factor = 1/2

Scale factor = 0.5.

Complete Question:

What scale factor will dilate triangle ABC so that it has the same vertices as triangle DEF?

Option 1: 0.25

Option 2: 0.5

Option 3: 1

Option 4: 2