Question

100 points.. please help?

this is my last question i have on my homework assignment. I'm unable to figure it out myself so help would be highly appreciated!! Thank-you!

Answer 1

The formula of a distance between two points:

We have the points J(-5, 6), K(3, 4) and L(-2, 1). Substitute:

The perimeter of ΔJKL:

The area of ΔJKL:

Explanation:

Answer 2

The fromula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have the points J(-5, 6), K(3, 4) and L(-2, 1). Substitute:

`|JK|=√((3-(-5))^2+(4-6)^2)=√(8^2+(-2)^2)=√(64+4)=√(68)\\\\=√(4\cdot17)=\sqrt4\cdot√(17)=2√(17)\\\\|JL|=√((-2-(-5))^2+(1-6)^2)=√(3^2+(-4)^2)=√(9+25)=√(34)\\\\|KL|=√((-2-3)^2+(1-4)^2)=√((-5)^2+(-3)^2)=√(25+9)=√(34)`

The perimeter of ΔJKL:

`P_(\Delta JKL)=|JK|+|JL|+|KL|\\\\P_(\Delta JKL)=2√(17)+√(34)+√(34)=2√(17)+2√(34)=2(√(17)+√(34))`

The area of ΔJKL:

`A_(\Delta JKL)=(1)/(2)|JL||KL|\\\\A_(\Delta JKL)=(1)/(2)\cdot√(34)\cdot√(34)=(1)/(2)(√(34))^2=(1)/(2)(34)=17`