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:
x = 10
Step-by-step explanation:
Answer:
<u><em>You just take it step by step by step. look it up for more information. </em></u>
<u><em>Hope this helps.</em></u>
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Answer:
25a^2-49
Step-by-step explanation:
1)use FOIL
F=first
O=out
I=inside
L=last
5a*5a+5a*-7+7*5a*7*-7
25a^2-35a+35a-49
25a^2-49
Hope this helps!
Answer:
The surface area of the pyramid is 466,137 squared cubits
Step-by-step explanation:
This is simply asking us to find the surface area of the square based pyramid with the given dimensions.
The first thing we need to know is the principle for finding the surface area of such pyramidal shapes. To get the surface area of a pyramid, we will have to add the base area to the area of the side faces ( lateral area)
The base area of the square based pyramid, will be the same as the area of a square which is = 453 cubits X 453 cubits =
The lateral area has already been given to us as 260,928 squared cubits.
The surface area of the pyramid is 260,928 + 205209 = 466137 squared cubits
Hence, the surface area of the pyramid is 466137 squared cubits
