Q. 225.0( 3 Votes )

If the vertices o

Answer :

We have the following triangle,

Let the vertices of the triangle be A(1,-3), B(4,p) and C(-9,7) be denoted by A(x1,y1), B(x2,y2) and C(x3,y3).


Area of the triangle where the vertices are given is,


Area = 1/2 [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]


And Area is given as 15 sq. units.


So,


1/2 [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] = �15


[x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] = �30


Substituting corresponding values in the equation, we get


[1(p – 7) + 4(7 – (-3)) + (-9)(-3 – p) = �30


[p – 7 + 40 + 27 + 9p = �30


60 + 10p = �30


10p = �30 – 60


p = ( �30 – 60)/10


So we have two solution, lets explore them.


I case: p = (30 – 60)/10


p = -30/10


p = -3


II case: p = (-30 – 60)/10


p = -90/10


p = -9


Hence, p has two values, they are -3 and -9.


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