Answer:
Option A , B and D are true.
The statement which are true:
The length of side AD is 4 units
The length of side A'D' is 8 units.
The scale factor is, [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given in figure trapezoid ABCD;
The coordinates of ABCD are:
A= (-4, 0)
B = (-2, 4)
C = (2,4)
D = (4, 0)
Since, trapezoid ABCD was dilated to create trapezoid A'B'C'D' as shown in figure;
The coordinates of A'B'C'D' are;
A' =(-2, 0)
B'=(-1, 2)
C' = (1, 2)
D' = (2, 0)
First calculate the length of AD
Using Distance formula for any two points i.e,
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Since, A = (-4, 0) and D = (4, 0)
then;
Length of AD = [tex]\sqrt{(4-(-4))^2+(0-0)^2} = \sqrt{(4+4)^2} =\sqrt{64}=8[/tex] units
Therefore, the length of side AD is, 8 units.
Similarly find the length of A'D'.
Where A' = (-2, 0) and D' =(2,0)
Using distance formula:
Length of A'D' = [tex]\sqrt{(2-(-2))^2+(0-0)^2} =\sqrt{(2+2)^2}= \sqrt{4^2} = 4[/tex]
Therefore, the length of side A'D' is, 4 units.
Now, find the slope of CD and C'D'
where C =(2, 4) , D = (4, 0) , C' = (1, 2) and D' =(2,0)
using slope formula for any two points is given by:
[tex]Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope of CD = \frac{0-4}{4-2} = \frac{-4}{2} = -2[/tex]
Similarly,
[tex]Slope of C'D' = \frac{0-2}{2-1} = \frac{-4}{2} = -2[/tex]
Since, Sides CD and C'D' have same slope i.e, -2
Scale factor(k) states that every coordinate of the original figure has been multiplied by the scale factor.
The rule for dilation with scale factor(k) is;
[tex](x, y) \rightarrow (kx , ky)[/tex]
To find the scale factor:
A = (-4, 0) and A' = (-2, 0)
[tex](-2, 0) \rightarrow (-4k , 0)[/tex]
On comparing we ghet;
-4k = -2
Divide -4 both sides we get;
[tex]k = \frac{1}{2}[/tex]
∴ The Scale factor is, [tex]k = \frac{1}{2}[/tex]
Since, k < 1 which implies the image is a reduction.
Therefore, the statements which are true regarding about trapezoids are;
The length of side AD is 4 units
The length of side A'D' is 8 units.
The scale factor is, [tex]\frac{1}{2}[/tex]
Answer:
A, B & E I just took the text
Step-by-step explanation: Ed 2021
