Question

if (k,2) (2,4) (3,2) are the vertices of a triangle of area 4sq units then the value of k is ​

Answer 1

Answer: 7

Step-by-step explanation:

By using area of a triangle formula,

1/2(x1(y2-y3)+x2(y3-y1)+x3(y1-y2))

We can find the value of k

Since the area of the triangle is already given,

Area=4sq units

We can equate the formula to 4 and find k,

1/2(k(4-2)+2(2-2)+3(2-4))=4

1/2(2k+0-6)=4

2k-6=8 (1/2 taken to rhs becomes x2)

2k=14

k=7

Answer 2

k=5

Step-by-step explanation:

a(k,2) b(2,4) c(3,2)

x1=k x2=2 x3=3

y1=2 y2=4 y3=2

∆of area=4sq

∆of area=1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)=0

4=1/2[k(4-2)+2(2-2)+3(2-4)=0

4=2k+0-6

4+6=2k

2k=10

k=10/2

k=5