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.
You just need to multiply 14 miles by 14 days so the answer is 196
After using the algebraic equation, the required value of x = 55/2.
WHAT IS ALGEBRIC EQUATION?
A mathematical statement wherein two expressions have been set equal to one another is known as an algebraic equation. A variable, coefficients, and constants make up an algebraic equation in most cases. Equations, or the equal sign, simply indicate equality. Equating each quantity with another is what equations are all about. Equations act as a scale of balance. If you've ever seen a balance scale, users know that for the scale to be deemed "balanced," an equal amount of weight must be applied to each side. The scale will tip to one side if we only add weight to one side, and the two sides will no longer be equally weighted.
(x-3)2 = 49
= x-3 = 49/2
= x = (49/2) + 3
= x = 55/2
So, the required value of x = 55/2.
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