Question

If the vertices of the triangle are (1,k), (4,-3), (-9,7) and its area is 15 sq. units, find the value of k.

Answer 1

The value of k is -3
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Answer 2

Given :

The vertices of the triangle are (1,k), (4,-3), (-9,7) and its area is 15 sq. units

To Find :

find the value of k.

Solution:

Vertices of triangle :

Coordinates of A = $(x_1,y_1)=(1,k)$

Coordinates of B =$(x_2,y_2)= (4,-3)$

Coordinates of C =$(x_3,y_3)= (-9,7)$

Area of triangle =$\frac{1}{2}|(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))|$

Area of triangle = $\frac{1}{2}|(1(-3-7)+4(7-k)+x_3(k-7))|$

We are given that its area is 15 sq. units.

$15=\frac{1}{2}|(1(-3-7)+4(7-k)-9(k-7))|$

30=|-10+28-4k-9k+63|

30=|81-13k|

13k=68

$k=\frac{68}{13}$

Hence the value of k is $\frac{68}{13}$