Question 1177582

Triangle {{{DEF}}} has vertices located at 

D ({{{2}}}, {{{1}}}), 
E ({{{3}}}, {{{5}}}), and 
F ({{{6}}}, {{{2}}}).

Part A: 

Find the length of each side of the triangle. Show your work.
the length of each side  is equal to the distance between endpoints

the length of the side {{{DE}}} is equal to the distance between ({{{2}}}, {{{1}}}) and ({{{3}}}, {{{5}}})

*[invoke formula_distance 2, 1, 3, 5]

so, {{{DE=4.12}}} (approximately)


the length of the side {{{DF}}} is equal to the distance between ({{{2}}}, {{{1}}}) and ({{{6}}}, {{{2}}})

*[invoke formula_distance 2, 1, 6, 2]

so, {{{DF=4.12}}} (approximately)

the length of the side {{{EF}}} is equal to the distance between (({{{3}}}, {{{5}}}) and ({{{6}}}, {{{2}}})

*[invoke formula_distance 3, 5, 6, 2]

{{{EF= 4.24}}}(approximately)



Part B: 

Find the slope of each side of the triangle. Show your work.

 {{{DE}}} passes through ({{{2}}}, {{{1}}}) and ({{{3}}}, {{{5}}})

slope is *[invoke slope 2, 1, 3, 5]

{{{DF}}} passes through ({{{2}}}, {{{1}}}) and ({{{6}}}, {{{2}}})

slope is *[invoke slope 2, 1, 6, 2]

side {{{EF}}} passes through (({{{3}}}, {{{5}}}) and ({{{6}}}, {{{2}}})
slope is *[invoke slope 6, 2, 3, 5]



Part C: 

Classify the triangle. Explain your reasoning.


Triangle {{{DEF}}} is an {{{isosceles}}} triangle because sides {{{DE}}} and {{{DF}}} are the same length.



{{{drawing ( 600, 600, -10,10, -10, 10,
circle(2,1,.12),locate(2,1,D),
circle(3,5,.12),locate(3,5,E),
circle(6,2,.12),locate(6,2,F),
green(line(2,1,3,5)), green(line(2,1,6,2)),blue(line(6,2,3,5)),
graph( 600, 600, -10,10, -10, 10, 0)) }}}