Question

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

Answer 1

15=1/2{1(-3-7)+4(7-k)-9(k+3)
=>30=-10+28-4k-9k-27
=>39=-13k
=>k=-3

Answer 2

Given that,

The vertices of triangle are (1,k), (4,-3), (-9,7).

$x_{1}=1$

$y_{1}=k$

$x_{2}=4$

$y_{2}=-3$

$x_{3}=9$

$y_{3}=7$

Area is 15 square units.

We need to calculate the value of k

Using formula of area

$A=\dfrac{1}{2}(x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}))$

Put to value into the formula

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

$30=(1((-3)-7)+4(7-k)+9(k-(-3)))$

$30=-10+28-4k+9k+27$

$5k=30+10-28-27$

$k=\dfrac{-15}{5}$

$k=-3$

Hence, The value of k is -3