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gavmur [86]
2 years ago
14

On a coordinate plane, triangles R S T and L M N are shown. Triangle R S T has points (5, 5), (2, 1), and (1, 3). Triangle L M N

has points (0, negative 1), (2, negative 4), and (negative 2, negative 3). How does the area of triangle RST compare to the area of triangle LMN
Mathematics
1 answer:
ivolga24 [154]2 years ago
3 0

Answer:

LMN has a larger area

Step-by-step explanation:

Given

RST

R =(5,5)

S= (2,1)

T = (1,3)

LMN

L = (0,-1)

M= (2,-4)

N= (-2,-3)

Required

Compare both areas

The area of triangle is:

Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|

For RST, we have:

Area = \frac{1}{2}|5*1 - 2*5 + 2*3 - 1*1 + 1*5 - 5*3|

Area = \frac{1}{2}|-10|

Remove absolute signs

Area = \frac{1}{2}*10

Area = 10

For LMN, we have:

Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|

Area = \frac{1}{2}|0*-4-2*-1+2*-3--2*-4--2*-1-0*-3|

Area = \frac{1}{2}|-14|

Remove absolute signs

Area = \frac{1}{2}*14

Area = 7

<em>By comparing both areas, we can conclude that LMN has a larger area</em>

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