Perhaps the easiest way to find the midpoint between two given points is to average their coordinates: add them up and divide by 2.
A) The midpoint C' of AB is
.. (A +B)/2 = ((0, 0) +(m, n))/2 = ((0 +m)/2, (0 +n)/2) = (m/2, n/2) = C'
The midpoint B' is
.. (A +C)/2 = ((0, 0) +(p, 0))/2 = (p/2, 0) = B'
The midpoint A' is
.. (B +C)/2 = ((m, n) +(p, 0))/2 = ((m+p)/2, n/2) = A'
B) The slope of the line between (x1, y1) and (x2, y2) is given by
.. slope = (y2 -y1)/(x2 -x1)
Using the values for A and A', we have
.. slope = (n/2 -0)/((m+p)/2 -0) = n/(m+p)
C) We know the line goes through A = (0, 0), so we can write the point-slope form of the equation for AA' as
.. y -0 = (n/(m+p))*(x -0)
.. y = n*x/(m+p)
D) To show the point lies on the line, we can substitute its coordinates for x and y and see if we get something that looks true.
.. (x, y) = ((m+p)/3, n/3)
Putting these into our equation, we have
.. n/3 = n*((m+p)/3)/(m+p)
The expression on the right has factors of (m+p) that cancel*, so we end up with
.. n/3 = n/3 . . . . . . . true for any n
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* The only constraint is that (m+p) ≠ 0. Since m and p are both in the first quadrant, their sum must be non-zero and this constraint is satisfied.
The purpose of the exercise is to show that all three medians of a triangle intersect in a single point.
Answer:
everyone will have 15 dogs each
Step-by-step explanation:
dogs:
1+2+3+4+5=15
humans:
54+38+3+1+4=100
100x15=1500 <<<how many dogs there are in total
1500%100=15 <<<how many each person will get if u add all the dogs and divide them evenly for each person
Answer: 29.2%
Step-by-step explanation:
The total surface area is 196.9 million square miles and out of this, land occupies 57.5 million square miles.
The probability that a meteorite would hit land is the percentage of and out of the entire planet area:
= Land area/ Total earth surface area
= 57.5/ 196.9
= 29.2%
Answer:
y = $100 + $25x
Step-by-step explanation:
y is the total cost
x is the number of months
The sign up fee is $100.
Each month would cost an additional $25 per month.
The total cost then would be the sign up fee plus the $25 for each month. Since we do not know the number of months, we will assign x.
So the equation would be:
y = $100 + $25x
