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?
16ty
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

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.

ankitprmr2 ankitprmr2 · Answer 2 · 2021-10-18T11:57:50+02:00

The correct option is c) A translation by the rule (x,y) - (x,y-9) and then a 180° clockwise rotation about the origin.

Step-by-step explanation:

The rules of rotation about the origin-

Under a [tex]180^\circ[/tex] clockwise rotation about the origin gives,

[tex](x,y)\rightarrow(-x,y)[/tex]

In the given image, point A(2,3) becomes A'(-2,6).

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.

Now, see the value of x remains the same but changes sign, now you just have to use the rule

[tex](x,y) \rightarrow(x,y-9)[/tex]

Hence, [tex](2,3)\rightarrow (2,-6)[/tex]

Therefore the correct option is c) A translation by the rule (x,y) - (x,y-9) and then a 180° clockwise rotation about the origin.

For more information, refer the link given below

https://brainly.com/question/20848941?referrer=searchResults