SOLUTION: a (5;5);(-7;1); and c (1;-7) are the vertices of triangle ABC.show that ABC is an isosceles triangle.

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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:






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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