Question 1180249
a) Is the above triangle a right triangle? Show all work using analytical geometry tools to help support your answer. [6M]


J( {{{1}}}, {{{2}}}), K({{{-3}}},{{{-1}}}) and L({{{0}}},{{{-5}}})


{{{drawing( 600, 600, -10, 10, -10, 10, 
circle(1,2,.12), locate(1,2,J(1,2)),
circle(-3,-1,.12), locate(-3,-1,K(-3,-1)),
circle(0,-5,.12), locate(0,-5,L(0,-5)),
green(line(1,2,-3,-1)),green(line(1,2,0,-5)),
green(line(0,-5,-3,-1)),
 graph( 600, 600, -10, 10, -10, 10, 0)) }}}


the above triangle {{{is}}} a right triangle


b) Find the perimeter of the triangle

first find side lengths

find {{{JK}}}

*[invoke formula_distance 1, 2, -3, -1] 

{{{JK=5}}}

find {{{KL}}}

*[invoke formula_distance 0, -5, -3, -1] 

{{{KL=5}}}


find {{{JL}}}


 *[invoke formula_distance 1, 2, 0, -5] 

 {{{JL=7.07}}}


perimeter is:

{{{P=5+5+7.07=17.07}}}