Question 397932

Given points A(0,0), B(4,8) and C(6,2) are the vertices of triangle ABC

a) Use the {{{distance}}} formula to compute the lengths of sides {{{AB}}},

{{{BC}}}, and {{{AC}}}. If two of those lengths are {{{equal}}}, the triangle 

{{{is}}}{{{ isosceles}}}.


A(0,0), B(4,8)...... side {{{AB}}}


*[invoke Distance_Formula_for_Coordinate_Plane 0, 0, 4, 8]



B(4,8) and C(6,2).........side {{{BC}}}


*[invoke Distance_Formula_for_Coordinate_Plane 4, 8, 6, 2]


{{{AC}}}


A(0,0)  and C(6,2).........side {{{AC}}}


*[invoke Distance_Formula_for_Coordinate_Plane 0, 0, 6, 2]


{{{AC=6.32455532033676}}}



so,   {{{AB = 8.94427190999916}}} is NOT equal{{{BC=6.32455532033676}}},   

but, {{{BC=6.32455532033676}}} and {{{AC=6.32455532033676}}} are equal in 

length , and the triangle {{{is}}} {{{ isosceles}}}


b) Use the {{{midpoint}}} formula with the endpoints of the base of the 

triangle. (The side whose length is not equal to that of either of the other 

two sides is the base of triangle ABC.)


{{{AB = 8.94427190999916}}} is the base of the triangle


*[invoke find_the_Midpoint 0, 0, 4, 8]


midpoint{{{D}}} is at (2,4)


c) Compute the {{{slope}}} of {{{CD}}} and of {{{AB}}}. There is a relationship 

between the slopes of perpendicular lines; do the slopes of {{{CD}}} and 

{{{AB}}} satisfy that relationship?



 the {{{slope}}} of {{{CD}}}



*[invoke slope 6, 2, 2, 4]


the slope is {{{m=-(1/2)}}}



the {{{slope}}} of {{{AB}}}


*[invoke slope 0, 0, 4, 8]

{{{m=2}}}

since the slope of {{{CD}}} is {{{m=-(1/2)}}} and the slope of {{{AB}}} is the slope 

is {{{m=2}}}, they satisfy a relationship between the slopes of perpendicular lines