Q4 of 23 Page 1

Solve any two sub-questions:

A(5,4), B(-3,-2) and C(1,-8) are the vertices of a triangle ABC. Find the equations of median AD and line parallel to AC passing through the point B.

The figure is as follows:


Given:


A = (5, 4)


B = (-3, -2)


C = (1, -8)


Segment AD is the median


D is the midpoint of BC


By midpoint formula




x = -2 / 2


x = -1




y = -10 / 2


y = -5


D = (-1, -5)


Equation of median AD is given as follows:


y – y1 = m × (x – x1)




m = 9 / 6


6 × (y – 4) = 9 × (x – 5)


6y – 24 = 9x – 45


9x – 6y – 21 = 0


3x – 2y – 7 = 0


Therefore the equation of median AD = 3x – 2y – 7 = 0


Slope of Line AC




m = -12 / -4


m = 3


Since the line BP is parallel to AC.


The slope of line BP is same as that of slope of line AC = 3


Equation of line BP


y – y1 = m × (x – x1)


y + 2 = 3 × (x + 3)


y + 2 = 3x + 9


3x – y + 7 = 0


Therefore the equation of line BP = 3x – y + 7 = 0


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