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Find equation of medians of triangle ABC whose vertices are A(2.5) B(-4,9) C (-2,-1)

A median is a line that passes through one vertex and bisects the opposite side.

So we have to find the mid-points of AB, BC and AC

mid point of AB, let's call it D

(2 - 4)/2 , (5 + 9)/2

D(-1, 7)

slope of median CD = (7 + 1)/(-1 + 2) = 8

Therefore equation of median CD

y + 1 = 8 (x + 2)

y = 8x + 15

8x - y + 15 = 0

In the same way you can find the other two medians. just use mid-point formula to know the point where the median bisects the side.

mid point of BC, let's call it E

(-4 - 2)/2 , (9 - 1)/2

E (-3, 4)

Proceed in this way.

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Where does the y come from??
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Find the equation of the triangle whose vortices are (2,5),(-4,9) mid(-2,-1)
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Given:

AD is a median of triangle ABC whose vertices are A(2,5) B(-4,9) and C (-2,-1)

To find:

The coordinates of D

Solution:

We have given the triangle with the coordinates

A(2,5) B(-4,9) and C (-2,-1)

And it is also mentioned that AD is the median of the triangle which means the median is the midpoint of the third side of the triangle

So, D must  be the midpoint of the BC of the ΔABC

So the coordinates of D(x,y) is given by:

x = (x1+x2)/2

  • x = (-4-2)/2
  • x = -6/2
  • x = -3

y = (y1+y2)/2

  • y = (9-1)/2
  • y = 8/2
  • y = 4

Hence the coordinates of the point D is (-3,4)

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