More help is appreciated:))
1 answer:
Step-by-step explanation:
You need to translate all the points to the right 3 and up 6
Therefore, you are going to use this formula:
(x,y) ⇾ (x + 3, y + 6)
This is the same format as the previous problem, if you have noticed.
Using this, plug in each coordinate, starting with P (5, -1)
(5, -1) ⇾ ( 5 + 3, -1 + 6)
(5, -1) ⇾ ( 8, 5 )
P = (8, 5)
Now point Q, (0, 8)
(0, 8) ⇾ (0 + 3, 8 + 6)
(0, 8) ⇾ ( 3, 14 )
Q = (3, 14)
And last but not least, the point R, (7, 5)
(7, 5) ⇾ (7 + 3, 5 + 6)
(7, 5) ⇾ ( 10, 11 )
R = (10, 11)
Therefore, P = (8, 5), Q
= (3, 14), R
= (10, 11) is your answer. This is the 4th option or D.
Hope this for you to understand this a bit more! =D
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Answer:
Emma's flight is farther from the airport
Step-by-step explanation:
Even without doing any detailed calculation, you can see on a graph that the larger turn Alice's flight makes keeps it closer to the airport.
Emma's flight is farther from the airport.
__
The distance can be calculated using the Law of Cosines. The angle of interest is the supplement of the turn angle. Since the leg distances are the same in each case, the only variable affecting the distance from the airport is the angle measure. Again, the larger the turn, the shorter the distance from the airport. If T is the turn angle, the distance is ...
d² = 100² +50² -2·100·50·cos(180° -T)
d² = 12500 +10000·cos(T) . . . . . . . using cos(180°-T) = -cos(T)
d = 100√(1.25+cos(T))
For Alice's 70° turn, the distance is ...
d = 100√(1.25+0.342) ≈ 126.18 mi
For Emma's 50° turn, the distance is ...
d = 100√(1.25 +0.643) ≈ 137.58 mi
Emma's flight is farther from the airport.
_____
The law of cosines formula is ...
c² = a² +b² -2ab·cos(C)
where triangle sides are lengths a, b, c and angle C is opposite side c.
