How can finding the slopes of MN and AB help in proving that MN is the midsegment of triangle ABC?
2 answers:
Answer: The slopes of two parallel lines are equal.
Step-by-step explanation: Let and
be the slopes of lines AB and MN respectively. We know that if the slopes of two parallel lines are equal, then the lines must be parallel. Thus, if we get
, then AB is parallel to MN. Also, if we already have M and N as the mid-points of AC and BC, the with the help of slopes of AB and MN, we arrive at our proof that MN is the mid-segment of Triangle ABC. Please see the figure for details.
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Answer:
Speed of Current = 5 miles per hour
Step-by-step explanation:
We know distance formula,
D = RT
Where
D is distance
R is rate
T is time
If we let speed of boat (assume) to be "x" and speed of current to be "c"
Then downstream rate is (with current) = x + c
Upstream rate is (against current) = x - c
40 mins to go 20 miles downstream, that means:
D = RT
20 = (x + c)(40)
and
60 minutes to go upstream, 20 miles, that means:
D = RT
20 = (x - c)(60)
Simplifying first equation:
40x + 40c = 20
Simplifying second equation:
60x - 60c = 20
Multiplying first equation by 60, we get:
60 * [40x + 40c = 20] = 2400x + 2400c = 1200
Multiplying second equation by 40, we get:
40 * [60x - 60c = 20] = 2400x - 2400c = 800
Now we add up both these equations:
2400x + 2400c = 1200
2400x - 2400c = 800
----------------------------------
4800x = 2000
x = 2000/4800 = 5/12
We need speed of current, that is "c", so we plug in the value of x into first equation and solve for c:
Speed of Current = 1/12 miles per minute
Since there is 60 minutes in an hours, that would be:
(1/12) * 60 = 5 miles per hour
Speed of Current = 5 miles per hour