Respuesta :
Answer:
The scale factor that transforms quadrilateral ABCD to quadrilateral A'B'C'D' is 3
Step-by-step explanation:
Quadrilateral ABCD has the following coordinates
A(1, 5), B(2, 6), C(3, 3) and D(1, 3)
The image A'B'C'D' has the following coordinates;
A'(-3, 1), B'(0, 4), C'(3, -5), D'(-3, -5)
The length of segment [tex]\overline {AB}[/tex] = √((2 - 1)² + (6 - 5)²) = √2
The length of segment [tex]\overline {BC}[/tex] = √((3 - 6)² + (3 - 2)²) = √10
The length of segment [tex]\overline {CD}[/tex] = √((1 - 3)² + (3 - 3)²) = 2
The length of segment [tex]\overline {DA}[/tex] = √((1 - 1)² + (3 - 5)²) = 2
For quadrilateral, we have;
A'(-3, 1), B'(0, 4), C'(3, -5), D'(-3, -5)
The length of segment [tex]\overline {A'B'}[/tex] = √(0 - (-3))² + (4 - 1)²) = 3·√2
The length of segment [tex]\overline {B'C'}[/tex] = √((3 - 0)² + (-5 - 4)²) = 3·√10
The length of segment [tex]\overline {C'D'}[/tex] = √((-3) - 3)² + (-5 - (-5))²) = 6
The length of segment [tex]\overline {D'A'}[/tex] = √((-3) - (-3))² + ((-5) - 1)²) = 6
The scale factor that transforms quadrilateral ABCD to A'B'C'D' is given as follows;
[tex]The \, scale \, factor \, of \, transformation = \dfrac{\overline {A'B'}}{\overline {AB}} = \dfrac{\overline {B'C'}}{\overline {BC}} = \dfrac{\overline {C'D'}}{\overline {CD}} = \dfrac{\overline {D'A'}}{\overline {DA}} = 3[/tex]
Therefore, the scale factor that transforms quadrilateral ABCD to A'B'C'D' = 3
