Answer:
The correct option is 2. The area of △RST is equal to the area of △LMN.
Step-by-step explanation:
If three vertices of a triangle are given, then the area of triangle is
[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
The vertices of triangle RST are R(5,5), S(2,1), T(1,3).
The area of △RST is
[tex]A=\frac{1}{2}|5(1-3)+2(3-5)+1(5-1)|[/tex]
[tex]A=\frac{1}{2}|-10-4+4|[/tex]
[tex]A=\frac{10}{2}[/tex]
[tex]A=5[/tex]
The area of △RST is 5 square unit.
The vertices of triangle LMN are L(0,-1), M(2,-4), N(-2,-3).
[tex]A=\frac{1}{2}|0(-4+3)+2(-3+1)-2(-1+4)|[/tex]
[tex]A=\frac{1}{2}|-4-6|[/tex]
[tex]A=\frac{10}{2}[/tex]
[tex]A=5[/tex]
The area of △LMN is 5 square unit.
The area of △RST is equal to the area of △LMN, therefore the correct option is 2.
