2020-2021 T-Math-Geo-T1-CBT: Section 1 - No Calculator Section Question: 1-4
Based on the graph below, which sequence of transformations is needed to carry ABCD onto its image A'BCD?
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8
A
D
В.
6
4
В
A
10
10 -8 -6 -4
4
6
8
10
-2
4
-6
-8
-101
A 180° clockwise rotation about the origin and then a reflection across the x-axis.
A reflection across the x-axis and then a translation by the rule (x, y) + (x-10, y + 9).
A translation by the rule (x, y) - (xy-9) and then a 180° clockwise rotation about the origin
A 90° clockwise rotation about the origin and then a reflection across the line y = x

A translation by the rule (x,y) - (x,y-9) and then a 180° clockwise rotation about the origin

Step-by-step explanation:

In order to solve this, you have to remember the rules of rotation about the origin, they state that under a 90º clockwise rotation about the origin the the coordinates would switch positions and one of them will change its sign, ( x, y ) becomes ( y, - x ), so if you check out the image you will notice that point A (2,3) becomes A' (-2,6) so since the coordinates changed not only switched you can figure out that this is not only rotation about the origin, but also a translation beforehand, since a 180º rotation about the origin will keep the values of the coordinates on each of them just changing both signs, this means that that is what we are looking for, since point A (2,3) becomes A' (-2,6), you can see the value of "x" remained the same but changed signs, now you just have to use the rule (x,y)-(x,y-9)

(2,3)=(2,3-9)

A' will be translated to (2,-6) if you do a 180º rotation about the origin on that point you will get (-2,6) cause you'd only need to change signs, that's why that is your answer.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies