Question

CAN YOU HELP ME FAST PLZ

Trapezoid ABCD was dilated to create trapezoid A'B'C'D'.

Answer 1

All of them are correct except the third option. The image is smaller than the pre-image after the dilations.

Answer 2

Options A, B, D and E are true.

Explanation:

In the figure attached, trapezoid ABCD is dilated to create trapezoid A'B'C'D'.

Option A.

Length of AD = Distance of A from the origin + Distance of D from the origin

= 4 + 4

= 8 units

Option A is true.

Option B.

Length of A'D' = Distance of A' from the origin + distance of D' from the origin

= 2 + 2

= 4 units

Option B is true.

Option C.

As we have measured in the options A and option B

`(AD)/(A'D')=(8)/(4)`

AD = 2× A'D'

So image is smaller than the pre image after dilation.

Option C is not true.

Option D.

Since coordinates of C and D are (2, 4) and (4, 0)

so the slope of CD =
`(y-y')/(x-x')`

=
`(4-0)/(2-4)`

=
`(4)/((-2))`

= (-2)

Now we know coordinates of C' and D' are (1, 2) and (2, 0)

Then slope of C'D' =
`(2-0)/(1-2)`

=
`(2)/(-1)=(-2)`

Therefore, slopes of CD and C'D' are same.

Option D is True.

Option E.

Scale factor =
`(A'D')/(AD)=(4)/(8)`

=
`(1)/(2)`

Option E is true.

Therefore, Options A, B, D and E are true.