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Question
If A (2, 2), B (−4, −4) and C (5, −8) are the vertices of a triangle, than the length of the median through vertex C is
Options
- \[\sqrt{65}\]
- \[\sqrt{117}\]
- \[\sqrt{85}\]
- \[\sqrt{113}\]
Solution
We have a triangle ΔABC in which the co-ordinates of the vertices are A (2, 2) B (−4,−4) and C (5,−8).
In general to find the mid-point P (x , y) of two points A(x1 , y1 ) and B (x2 , y2) we use section formula as,
`P(x , y) = ((x_1 + x_2 )/2 , (y_1 + y_2 ) / 2)`
Therefore mid-point D of side AB can be written as,
`D(x ,y ) = ((2-4)/2 , (2-4)/2)`
Now equate the individual terms to get,
x = -1
y = - 1
So co-ordinates of D is (−1,−1)
So the length of median from C to the side AB,
`CD = sqrt((5 +1)^2 + (-8 + 2)^2)`
`= sqrt(36 + 49 )`
`= sqrt(85)`
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