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:
An average chicken breast weighs 174 g, or about 6 ounces (oz). But sizes vary from smaller cuts at around 4 oz, to larger ones at 8 to 10 oz. There's no right or wrong choice here. It really depends on what you're cooking and how much chicken you want.
Answer:
(y - 25) = - 0.25(x - 20)
Step-by-step explanation:
Given that :
Height of candle after burning for 20 minutes = 25 cm
Height after burning for 1 hr (60 minutes) = 10 cm
Height (y) in cm of candle x minutes after being lit:
Using the equation :
(y - y1) = m(x - x1)
m = (change in y / change in x)
Change in height within 60 minutes :
Height at 20 minutes = 25cm
Height after an hour = 10
Change in height per hour = (25 - 10) = 15cm
Hence, m = change in height per minute
15cm / 60 = 0.25cm ( - 0.25) (decrease in height)
y1 = 25 ; x1 = 20
(y - y1) = m(x - x1)
(y - 25) = - 0.25(x - 20)
Try using PEMDAS,
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
So just do the problem in that order.
Answer:
y=(-5/3)x+29
Step-by-step explanation:
we will use the base formula y=mx+b
In order to be perpendicular, the slope must be the flipped fraction and have the opposite sign, so our m is (-5/3)
y=(-5/3)x+b
You can plug in the (9,14) point in order to find the b
14=(-5/3)(9)+b
14=(-45/3)+b
14=(-15)+b
14+15=b
29=b
and so altogether our equation is y=(-5/3)x+29
