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:
8
Step-by-step explanation:
24 = 2* 2 * 2 * 3
40 = 2 * 2 * 2 * 5
GCF = 2*2*2 = 8
Answer:
P is complementary to x
Step-by-step explanation:
Complementary means adding to 90 degrees
P+x = 90 degrees
So P is complementary to x
Answer: multiply x by 2 in the first equation and subtract the second equation
Step-by-step explanation:
To solve a system of linear equations by elimination method , our first step is to make its (either x or y) coefficient same.
For that we multiply a number to both sides of the equation not to only one term.
So by checking all the given options it is pretty clear that the last option is not applicable for elimination method because in this 2 is multiplied to only one term, which proceeds to loose the balance of the equation.
Thus , an INCORRECT step that will NOT produce a system with the same solution is "multiply x by 2 in the first equation and subtract the second equation
".
Answer:
y= 5x+2
Explanation:
slope is 5 and the y-intercept is 2.
