Question

Show that the following points form an isosceles triangle.

(1, - 2), ( - 5, 1) and (1, 4)

Answer 1

first mark the points on the graph and then draw the lines according to points and then join all the lines and you will get an isosceles triangle.
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Answer 2

using distance formula to get distance between co - ordinates (x,y) and (a,b)
so√{(a - x)² + (b - x)²}
let co - ordinate (1, -2 ) be A (-5,1 ) be B and (1,4) be C
we know that in isosceles triangle length of two sides are equal 
so we have to show that the distance between any two points are equal
so distance between co - ordinate (1, -2) and (-5 , 1)  i.e. AB 
 is √{(-5 - 1)² +(1 - (-2)) ²}
 =√(36 + 9 )    =√(45) units
so distance between co - ordinate (1.-2) and (1,4) i.e. AC is
 √{(1 - 1)² +(4-(-2)) }
=√(0 + 36 )= √36 = 6 units
so distance between co - ordinate (-5 , 1) and (1,4)  i.e. BC
is √{(1- (-5))² + (4 - 1 )²}
= √(36 + 9) =√45 units so 
we can see distance of AB and BC are same so it is a isosceles triangle
PROVED