find the value of k so that area of triangle ABC with A (k + 1, 1),B(4, - 3) and C (7 ,-k) is 6 square units
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Heya
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Area of Trangle having co-ordinates (x1, y1 ) , ( x2 , y2) and ( x3 , y3 ) is
=>
1/2 {x1( y2 - y3 ) -x2 ( y1-y3 ) + x3(y1-y2)}
=>
1/2{(k+1)(-3+k)-4(1+k)+28}=6
=>
-3k + k² - 3 + k -4 -4k = -16
=>
k² -6k + 9= 0
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k² -3k -3k + 9 = 0
=>
k( k - 3 ) -3 ( k - 3 ) = 0
=>
( k - 3 ) = 0 or ( k - 3 ) = 0
k = 3
_______________________________
Area of Trangle having co-ordinates (x1, y1 ) , ( x2 , y2) and ( x3 , y3 ) is
=>
1/2 {x1( y2 - y3 ) -x2 ( y1-y3 ) + x3(y1-y2)}
=>
1/2{(k+1)(-3+k)-4(1+k)+28}=6
=>
-3k + k² - 3 + k -4 -4k = -16
=>
k² -6k + 9= 0
=>
k² -3k -3k + 9 = 0
=>
k( k - 3 ) -3 ( k - 3 ) = 0
=>
( k - 3 ) = 0 or ( k - 3 ) = 0
k = 3
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