For part A: two transformations will be used. First we will translate ABCD down 3 units: or the notation version for all (x,y) → (x, y - 3) so our new coordinates of ABCD will be:
A(-4,1)
B(-2,-1)
C(-2,-4)
D(-4,-2)
The second transformation will be to reflect across the 'y' axis. Or, the specific notation would be: for all (x,y) → (-x, y) New coordinates for A'B'C'D'
A'(4,1)
B'(2,-1)
C'(2,-4)
D'(4,-2)
Part B: The two figures are congruent.. We can see this a couple of different ways.
- first after performing the two transformations above, you will see that the original figure perfectly fits on top of the image.. exactly the same shape and size.
- alternatively, you can see that the original and image are both parallelograms with the same dimensions.
Answer:
a) 
b) 
Step-by-step explanation:
Use logarithm properties:
Then
a) 
b) 
Answer:
y = 2x - 3
Step-by-step explanation:
Parallel lines have the same slope
only the constant changes
y = 2x + b
To find "b"
Plug in point (3, 3)
3 = 2(3) + b
3 = 6 + b
Subtract 6 from both sides
-3 = b
The equation for the parallel line is
y = 2x - 3
1) -13 = -4a - 2b + c
-13 = -2(2a + b) + c
2) 3 = 4a + 2b +c
3 = 2(2a + b) + c
3) 5 = 16a + 4b + c
5 = 4(4a + b) + c
[ Final Answers are in bold ]
Hope this helps!
Two polygons are similar if their corresponding angles are congruent and their sides are in proportion.
The sides could be in a ration of 1:1 in which case the two hexagons have corresponding sides that are congruent, but they do not have to be. It could be the case that the sides of one are twice the length of the other so the ratio is 2:1. In this case the hexagons have the same shape but not the same size.
So the answer is this, the corresponding sides of similar hexagons may be congruent but do not have to be.
