The area of triangle is 7 square units, which is mentioned in option B. It is obtained from the given diagram.
Step-by-step explanation:
The given is,
For above question diagram is missing, so i attach the diagram.
Step:1
Formula for area of triangle from the coordinates,
[tex]A =\frac{1}{2} [ x_{1}(y_{2} -y_{3})+x_{2} (y_{3}-y_{1} )+x_{3}(y_{1} - y_{2} )][/tex].............(1)
Where,
[tex](x_{1} ,y_{1} ),(x_{2} ,y_{2} ), (x_{3} ,y_{3} )[/tex] are coordinates
From the given,
A ( 1, 1 ) - [tex](x_{1} , y_{1} )[/tex]
B ( 4, 0 ) - [tex](x_{2} , y_{2} )[/tex]
C ( 3, 5 ) - [tex](x_{3} , y_{3} )[/tex]
Equation (1) becomes,
Area, [tex]A = \frac{1}{2} [1(0-5)+4(5-1)+3(1-0)][/tex]
[tex]= \frac{1}{2} [1(-5)+4(4)+3(1)][/tex]
[tex]= \frac{1}{2} [ -5 +16 + 3][/tex]
[tex]= \frac{1}{2} (14)[/tex]
= 7
Area of triangle, A = 7 square units
Result:
The area of triangle is 7 square units, which is mentioned in option B. It is obtained from the given diagram.
