Answer:
LMN has a larger area
Step-by-step explanation:
Given
RST
[tex]R =(5,5)[/tex]
[tex]S= (2,1)[/tex]
[tex]T = (1,3)[/tex]
LMN
[tex]L = (0,-1)[/tex]
[tex]M= (2,-4)[/tex]
[tex]N= (-2,-3)[/tex]
Required
Compare both areas
The area of triangle is:
[tex]Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|[/tex]
For RST, we have:
[tex]Area = \frac{1}{2}|5*1 - 2*5 + 2*3 - 1*1 + 1*5 - 5*3|[/tex]
[tex]Area = \frac{1}{2}|-10|[/tex]
Remove absolute signs
[tex]Area = \frac{1}{2}*10[/tex]
[tex]Area = 10[/tex]
For LMN, we have:
[tex]Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|[/tex]
[tex]Area = \frac{1}{2}|0*-4-2*-1+2*-3--2*-4--2*-1-0*-3|[/tex]
[tex]Area = \frac{1}{2}|-14|[/tex]
Remove absolute signs
[tex]Area = \frac{1}{2}*14[/tex]
[tex]Area = 7[/tex]
By comparing both areas, we can conclude that LMN has a larger area
