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

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.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

the answer is y = 11.54

hope this : )