Question

100 points.. please help?

Answer 1

The fromula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

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

The perimeter of ΔJKL:

$P_{\Delta JKL}=|JK|+|JL|+|KL|\\\\P_{\Delta JKL}=2\sqrt{17}+\sqrt{34}+\sqrt{34}=2\sqrt{17}+2\sqrt{34}=2(\sqrt{17}+\sqrt{34})$

The area of ΔJKL:

$A_{\Delta JKL}=\dfrac{1}{2}|JL||KL|\\\\A_{\Delta JKL}=\dfrac{1}{2}\cdot\sqrt{34}\cdot\sqrt{34}=\dfrac{1}{2}(\sqrt{34})^2=\dfrac{1}{2}(34)=17$