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A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle are drawn below.

Note that the three medians appear to intersect at the same point! Let's try this out with a particular triangle. Consider the triangle ABC with A=(3,6), B=(-5,2), and C=(7,-8).

(a) Let D,E,F be the midpoints of BC, AC, AB respectively. Find the equations of medians AD, BE, and CF.

(b) Show that the three medians in part (a) all pass through the same point.

 

 Sep 20, 2020
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hat does it stand for?

Slope or
Gradienty when x=0
(see Y Intercept)

 

y = how far up

x = how far along

m = Slope or Gradient (how steep the line is)

b = value of y when x=0

How do you find "m" and "b"?

b is easy: just see where the line crosses the Y axis.

m (the Slope) needs some calculation:

m = Change in YChange in X 

 

Knowing this we can work out the equation of a straight line:

Example 1


 

m = 21 = 2

b = 1 (value of y when x=0)
 

So: y = 2x + 1

With that equation you can now ...

... choose any value for x and find the matching value for y

For example, when x is 1:

y = 2×1 + 1 = 3

Check for yourself that x=1 and y=3 is actually on the line.

Or we could choose another value for x, such as 7:

y = 2×7 + 1 = 15

And so when x=7 you will have y=15

 Sep 21, 2020

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