Describe fully the single transformation which takes shape A to shape B.
2 answers:
Answer:
Clockwise rotation 90° about the center of (4,3)
Step-by-step explanation:
A, B, C: (1,6) (3,8) (5,6) -> A'B'C' (7,6) (9,4) (7,2)
clockwise 90° rotation formula:
x' = (y - y₀) + x₀ x: original x₀: center
y' = - (x - x₀) + y₀
For A (1,6) -> A' (7 , 6)
7 = (6 - y₀) + x₀ x₀ - y₀ = 1 ... (1)
6 = - (1 - x₀) + y₀ x₀ + y₀ = 7 ... (2)
(1) + (2): 2 x₀ = 8 x₀ = 4
(2)-(1): 2 y₀ = 6 y₀ = 3
Rotation center: (4 , 3)
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Answer:
(A)The northern lighthouse is 8.2 miles closer than the southern lighthouse.
Step-by-step explanation:
The triangle attached represents the given problem.
First, let us determine the distance of the Boat from each of the lighthouse.
In Triangle ABC,
∠A+∠B+∠C=180 degrees
21+∠B+16=180
∠B=180-37=143 degrees.
Using Law of Sines
Similarly
Difference in Distance =35.73-27.48=8.25 miles
Therefore, the northern lighthouse is 8.2 miles closer than the southern lighthouse.
