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:
y ≈ 5.63
Step-by-step explanation:
m∠KLN and m∠NLM have to add up to m∠KLM
m∠KLN = 47°
m∠NLM = 16y°
m∠KLM = 137°
47 + 16y = 137
16y = 90
y = 45/8
y = 5.625
y ≈ 5.63
Answer:
what equation
Step-by-step explanation:
what equation
Answer:
The length of the case is 24 cm and its width is 17cm.
Step-by-step explanation:
The Length of a standard jewel case is 7cm more than its width.
Let the length be represented by L and the width be represented by W, this means that:
L = 7 + W
The area of the rectangular top of the case is 408cm². The area od a rectangle is given as:
A = L * W
Since L = 7 + W:
A = (7 + W) * W = 7W + W²
The area is 408 cm², hence:
408 = 7W + W²
Solving this as a quadratic equation:
=> W² + 7W - 408 = 0
W² + 24W - 17W - 408 = 0
W(W + 24) - 17(W + 24) = 0
(W - 17) (W + 24) = 0
=> W = 17cm or -24 cm
Since width cannot be negative, the width of the case is 17 cm.
Hence, the length, L, is:
L = 7 + 17 = 24cm.
The length of the case is 24 cm and its width is 17cm.
