Question

How does the area of triangle RST compare to the area of triangle LMN?

The area of △RST is 2 square units less than the area of △LMN.
The area of △RST is equal to the area of △LMN.
The area of △RST is 2 square units greater than the area of △LMN.
The area of △RST is 4 square units greater than the area of △LMN.

Answer 1

The answer is the letter B or The area of △RST is equal to the area of △LMN.

Explanation:

Answer 2

The correct option is 2. The area of △RST is equal to the area of △LMN.

Explanation:

If three vertices of a triangle are given, then the area of triangle is

`A=(1)/(2)|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|`

The vertices of triangle RST are R(5,5), S(2,1), T(1,3).

The area of △RST is

`A=(1)/(2)|5(1-3)+2(3-5)+1(5-1)|`

`A=(1)/(2)|-10-4+4|`

`A=(10)/(2)`

`A=5`

The area of △RST is 5 square unit.

The vertices of triangle LMN are L(0,-1), M(2,-4), N(-2,-3).

`A=(1)/(2)|0(-4+3)+2(-3+1)-2(-1+4)|`

`A=(1)/(2)|-4-6|`

`A=(10)/(2)`

`A=5`

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.