Answer:
A' = (0,0)
B'=(8,0)
C'=(8,2)
D'=(0,2)
It is not a rigid motion.
Step-by-step explanation:
To use the mapping rule, substitute the original x and y values in it.
The coordinates of A are (0,0).
Using the mapping rule, the x coordinate of A' = 2x0 = 0
Using the mapping rule, the y coordinate of A' = (1/2)x0=0
So A' will not change locations. The image will be at (0,0).
The coordinates of B are (4,0)
Using the mapping rule, the x-coordinate of B' = 2x4 = 8
Using the mapping rule, the y-coordinate of B' = (1/2)x0=0
Therefore the image of B' will be located at coorindate (8,0)
The coorindates of C are (4,4).
Using the mapping rule, the x-coordinate of C' = 2x4=8
Using the mapping rule, the y-coordinate of C' = (1/2)x4=2
Therefore the image of C' will be located at coordinate (8,2)
The coordinates of D are (0,4)
Using the mapping rule, the x-coordinate of D' = 2x0 = 0
Using the mapping rule, the y-coordinate of D' = (1/2)x4=2
Therefore the image of D' will be located at coordinate (0,2)
<em>Is the transformation a rigid motion?</em>
NO, this transformation is not a rigid motion because the relative distance between the points does not stay the same after they have been transformed. The transformation is not a translation , rotation, reflection, nor glide reflection.
Well, let's first solve each equation:
1.) -4x + 6 - 3x = 12 - 2x - 3x
To start, combine each like-term on each side of the equal sign (The numbers with variables in-common // the numbers alike on the same side of the equal sign):
-7x + 6 = 12 - 5x
Now, we get the two terms with variables attached to them, on the same side, so, we do the opposite of subtraction, which is, addition:
-7x + 6 = 12 - 5x
+5x +5x
_____________
-2x + 6 = 12
Next, you do the opposite of addition, which is, subtraction, and, subtract 6 from both sides:
-2x + 6 = 12
-6 -6
____________
-2x = 6
Finally, divide by -2 on each side, to find out what the value of 'x' is:
-2x = 6
÷-2 ÷-2
________
x = -3
So, the answer is not 'A.'
_________________________________________
Now, we test out the rest of the equations, the exact same way:
2.) 4x + 6 + 3x = 12 + 2x + 3x
Combine your like-terms, on each side of the equal sign:
7x + 6 = 12 + 5x
Now, get both terms, with the variable, 'x,' to the same side, and, to do that, do the opposite of addition, which is, subtraction:
7x + 6 = 12 + 5x
-5x -5x
______________
2x + 6 = 12
Next, subtract 6 from both sides:
2x + 6 = 12
-6 -6
__________
2x = 6
Finally, divide by 2, on both sides:
2x = 6
÷2 ÷2
__________
x = 3
So, the answer is 'B.'
_________________________________________
3.) 4x + 6 - 3x = 12 - 2x - 3x
Again, we combine the like-terms, on both sides of the equal sign:
x + 6 = 12 - 5x
Now, we get both terms with the variable 'x,' to the same side, and, the opposite of subtraction, is addition, so, we're going to add 5x to both sides:
x + 6 = 12 - 5x
+ 5x + 5x
______________
6x + 6 = 12
Now, we subtract 6 from each side, because, the opposite of addition, is subtraction:
6x + 6 = 12
- 6 - 6
_____________
6x = 6
Now, divide by 6, on both sides:
6x = 6
÷ 6 ÷ 6
_____________
x = 1
So, the answer is not 'C.'
_________________________________________
4.) 4x + 6 - 3x = 12x + 2x + 3x
First, we combine the like-terms:
x + 6 = 17x
Next, we get both terms, with the variable, 'x,' to the same side:
x + 6 = 17x
-x -x
_____________
6 = 16x
Now, divide by 16, on both sides:
X = 3/8
So, 'D,' is not the answer.
_______________________
The answer is, 'B.'
I hope this helps!
