Question

A(5, 3), B(-1, 1) and C(7, -3) are the vertices of a triangle ABC. If P is the mid-point of AB and Q is the mid point of AC,show that PQ=1/2BC​

Answer 1

Step-by-step explanation:

area of a triangle =1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

=1/2|5(1-(-3))+-1(-3)-3)+7(3-1)|

= 1/2|5(4)-1(6)+7(2)

= 1/2|20-6+14|

=1/2|14-14|

=1/2

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Answer 2

Answer:

L = [ (5-1)/2, (3+1)/2 ] = (2, 2)                   formula for midpoint: [ (x1+x2)/2 ,  (y1+y2)/2 ]

M = [ (5+7)/2, (3-3)/2 ] = (6, 0)

LM² = (6-2)² + (0-2)² = 20             =>   LM = 2√5     as    distance² = (x1-x2)²+(y1-y2)²

BC² = (7+1)² + (-3-1)² = 80    =>   BC = 4√5

Hence  LM = BC/2