Answer :

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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