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Show that the following points form an isosceles triangle.

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

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

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i hope it will help u!!!!!!

plz mark as best!!!!!!!!!!!

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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

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