Hi

 

A. Show that triangle ABC is an isosceles triangle

B(4,8) and C(6,2)                       A(0,0) and C(6,2)

distance AB = = distance AC = 



B. Find the coordinates of D , the midpoint of the base AB

A(0,0) and B(4,8)

Midpoint(, ) (4/2,8/2) OR PT(2,4)



C. Show that CD is perpendicular to AB

 m of CD = 

 m of AB = 8/4 = 2

 SLOPES negative reciprocals, lines perpendicular



 

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
 

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



a) Use the  formula to compute the lengths of sides ,



, and . If two of those lengths are , the triangle 



.





A(0,0), B(4,8)...... side 







 
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

  

  

  

  Thus in our case, the required distance is

  

  

  

  For more on this concept, refer to Distance formula.

  









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







 
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

  

  

  

  Thus in our case, the required distance is

  

  

  

  For more on this concept, refer to Distance formula.

  













A(0,0)  and C(6,2).........side 







 
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

  

  

  

  Thus in our case, the required distance is

  

  

  

  For more on this concept, refer to Distance formula.

  















so,    is NOT equal,   



but,  and  are equal in 



length , and the triangle  





b) Use the  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.)





 is the base of the triangle







 
Solved by pluggable solver: Find the Midpoint
Let C=the midpoint





















Therefore,



The midpoint C is located at (2,4)











midpoint is at (2,4)





c) Compute the  of  and of . There is a relationship 



between the slopes of perpendicular lines; do the slopes of  and 



 satisfy that relationship?







 the  of 









 
Solved by pluggable solver: Finding the slope


  

  Slope of the line through the points (6, 2) and (2, 4)

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  Answer: Slope is 

  

  







the slope is 







the  of 







 
Solved by pluggable solver: Finding the slope


  

  Slope of the line through the points (0, 0) and (4, 8)

  

  

  

  Answer: Slope is 

  

  









since the slope of  is  and the slope of  is the slope 



is , they satisfy a relationship between the slopes of perpendicular lines





 

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