Question

If the area of triangle abc with vertices [x,3] [4,4] and [3,5] is 4 sq units find x

Answer 1

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Answer 2

Answer:

x = -3

Step-by-step explanation:

Given,

Vertices of triangle = [x,3] [4,4] and [3,5]

Area of triangle = 4 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 = 4

Substituting the values of vertices and Area ,

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

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

$\frac{1}{2} [ -x+8-3]$ = 4

$\frac{1}{2} [ -x+5]$ = 4

$\frac{-x+5}{2}$ = 4

-x + 5 = 8

-x = 3

x = -3

Hence,

x = -3