A (2, 3), B (-2, 1) and C (4, -3) are the vertices of ΔABC. Find the slope of
(i) side AB
(ii) altitude through A
(iii) median through A
(iv) perpendicular bisector of AB.
Answers
Formula of slope
We know that formula of slope (between x1,y1 and x2,y2 ) is :
( y2 - y1 ) / ( x2 - x1 )
Slope of AB
Side AB slope = ( y2 - y1 ) / ( x2 - x1 )
= ( 1 - 3 ) / ( 2 + 2 )
= - 2 / 4
= - 1 / 2
Slope = - 1/2
Altitude through A
Slope of BC = ( y2 - y1 ) / ( x2 - x1 )
= ( 1 + 3 ) / ( -2 - 4 )
= - 4 / 6
= -2 / 3
Slope of BC's altitude = - 1/ slop of BC
= -1/2/3
= 3/2
Slope = 3/2
Median through A.
Median divides through A divides the opposite side BC
Midpoint of BC = ( x1` + x2 ) / 2 , ( y1 + y2 ) / 2 [ Midpoint formula ]
= ( 4 - 2 ) / 2 , ( - 3 + 1 ) / 2
= 2/2 , -2/2
= 1 , - 1
Slope of the median = ( y2 - y1 ) / ( x2 - x1 )
= ( -1 - 3 ) / ( 1 - 2 )
= - 4/-1
= 4
Slope = 4
Bisector of AB
Slope of bisector = - 1/ slope of AB
= - 1 / -1/2
= 2
Slope = 2
Hope it helps :)
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