Question

the area of the triangle formed by the points by using heron formula (1,1) ,(1,4)and (5,1)​

Answer 1

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Answer 2

Answer:

126.55 sq units

Step-by-step explanation:

The Distance Formula =√[(x1-x2)²-(y1-y2)²]The Heron's Formula =√[s(s-a)(s-b)(s-c)]

Step-by-step explanation:

Let A(x1,y1)=(1,1)    B(x2,y2)=(1,4)     C(x3,y3)=(5,1)

By using distance formula ,

AB = √[0+9] =3units

BC = √[16+9] =5units

AC = √[16-0] =4units

Now it's time to apply heron's formula for the 3 sides of the triangle,

√[s(s-a)(s-b)(s-c)]

Here s=semiperimeter of the traiangle = [AB+BC+AC]/2 = 32/2=16units

Let AB=a , BC=b , CA=c

Then substituting in the formula and simplifying,

=√[16(16-3)(16-5)(16-9)]

=√{16*13*11*7}

=√16016

=126.55 square units

Hope it helps you