Question 970876: a (5;5);(-7;1); and c (1;-7) are the vertices of triangle ABC.show that ABC is an isosceles triangle.
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! a ( , ); b ( , ); and c (,) are the vertices of triangle ABC
to show that ABC is an  triangle, we need to show that the distance between two vertices is  ; so, use the distance formula
the distance between  and 
a (, );
b (,)
or
the distance between and 
a (, );
c (,)
or
as you can see,  => so, ABC is an triangle
let's draw it too
first find equation of a line through each two points:
a line through points and
| Solved by pluggable solver: Find the equation of line going through points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (5, 5) and (x2, y2) = (-7, 1).
Slope a is  .
Intercept is found from equation  , or  . From that,
intercept b is  , or  .
y=(0.333333333333333)x + (3.33333333333333)
Your graph:
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a line through points and
| Solved by pluggable solver: Find the equation of line going through points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (5, 5) and (x2, y2) = (1, -7).
Slope a is  .
Intercept is found from equation , or  . From that,
intercept b is , or  .
y=(3)x + (-10)
Your graph:
|
a line through points and
| Solved by pluggable solver: Find the equation of line going through points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-7, 1) and (x2, y2) = (1, -7).
Slope a is  .
Intercept is found from equation , or  . From that,
intercept b is , or  .
y=(-1)x + (-6)
Your graph:
|
so, equations are:
graph all together:
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