Question

the vertices of a triangle are (3,4),(m,2) and (5,6).if its area is 2square units,find m

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The value of m is 3

Step-by-step explanation:

Given,

Vertices of triangle = [3,4] [m,2] and [5,6]

Area of triangle = 2 sq units

Since we know,

Area of triangle having 3 vertices is :

( x₁ , y₁ ) , ( x₂ , y₂ ) and ( x₃ , y₃ ) is given by formula :

$\frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]$

We are given area = 2

Substituting the values of vertices and Area ,

$\frac{1}{2}[3(2-6)+m(6-4)+5(4-2)]$ = 2

$\frac{1}{2}[3(-4)+m(2)+5(2)]$ = 2

$\frac{1}{2}[(-12)+2m+10]$ = 2

$\frac{1}{2}[-2+2m]$ = 2

-1 + m = 2

m = 2 + 1

m = 3

Hence,

The value of m is 3