A(5,-3),B(8,2) and C(0,0) are the vertices of a triangle .show that the median from A is perpendicular to the side BC
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Median from A is perpendicular to the side BC if A(5,-3),B(8,2) and C(0,0) are the vertices of a triangle
Step-by-step explanation:
A(5,-3),B(8,2) and C(0,0) are the vertices of a triangle
Let AD is median
=> D is mid point of BC
D = (8 + 0)/2 , (2 + 0)/2 = 4 , 1
Slope of AD = ( 1 -(-3))/(4 - 5) = 4/(-1) = - 4
Slope of BC = ( 2 - 0)/(8 -0) = 2/8 = 1/4
Two lines are perpendicular if multiplication of their slope = -1
Slope of AD * Slope of BC
= -4 * (1/4)
= - 1
=> AD ⊥ BC
Median from A is perpendicular to the side BC
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