"quadrilateral abcd underwent a sequence of transformations to give quadrilateral a′b′c′d′. which transformations could have taken place?

a reflection across the x-axis followed by a reflection across the y-axis

a translation 10 units down followed by a translation 8 units to the right

a rotation 90° counterclockwise about the origin followed by a reflection across the y-axis

a reflection across the line y = x followed by a reflection across the line y = -x"

The transformation that had taken place to map Quadrilateral ABCD to Quadrilateral A'B'C'D' is:

     A translation 10 units down followed by a translation 8 units    to the right

We are given a vertices of Quadrilateral ABCD as:

A(-6,4) , B(-6,6) , C(-2,6) , D(-4,4)

Now when translation is  done 10 units down  then the rule that follows this transformation is:

                 (x,y) → (x,y-10)

and coordinate of the transformed image will be:

A(-6,4) → A°(-6,-6)

B(-6,6) → B°(-6,-4)

C(-2,6) → C°(-2,-4)

D(-4,4) → D°(-4,-6)

Now when this image is translated 8 units to the right we obtain image A'B'C'D' and the coordinates of the transformed image follows the rule:

                       (x,y) → (x+8,y)

Hence,

A°(-6,-6) → A'(2,-6)

B°(-6,-4) → B'(2,-4)

C°(-2,-4) → C'(6,-4)

D°(-4,-6) → D'(4,-6)

Hence,

A(-6,4) → A'(2,-6)

B(-6,6) → B'(2,-4)

C(-2,6) → C'(6,-4)

D(-4,4) → D'(4,-6)

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

the function makes a strait line horizontally with no x intercept but a y intercept at 9.