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:
Step-by-step explanation:
<h3>#4</h3>
According to diagram we have
- QR ≅ QT
- QS ≅ QS (common side)
- QSR ≅ QST (both right angles)
Considering above we can state
- QSR ≅ QST by HL (hypotenuse-leg)
<h3>#5</h3>
Two angles are congruent but the order of angles is not same
Triangles are not similar.
<h3>#6</h3>
Two angles and a side are congruent but the order of angles is not same.
Triangles are not similar.
To answer this, we need to see the polynomial. Descending order is in a way that the first term of the polynomial will be three, the second (in descending order, two....and so on).
420t+20t3-210t2
In descending order is:
20t^3 - 210t^2 + 420t
So, the option is number two.
Answer:
2
Step-by-step explanation:
2
Answer:
ab² - 9
Step-by-step explanation:
Given in the question an expression
(ab + 3)(ab - 3)
To product mentally we will use polynomial identity called
Difference of squares
<h3>a² - b² = (a+b)(a-b) </h3>
here a = ab
b = 3
(ab + 3)(ab - 3) = ab² - 3² = ab² - 9
