Question

prove that the point (7,10) , (4,5) and (10,15) are the vertices of an isosceles triangle​

Answer 1

Answer:

Let the vertices of an isosceles right triangle be A(7,10), B(-2,5) and C(3,-4)

So by distance formula we have,

Distance between two points =

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

AB=

(−2−7)

2

+(5−10)

2

=

81+25

=

106

BC=

(3+2)

2

+(−4−5)

2

=

(25+81)

=

106

AC=

(3−7)

2

+(−4−10)

2

=

−16+196

=

212

∴AB=BC⇒ This implies that ABC is an isosceles triangle.

Also,

AB

2

+BC

2

=106+106=212

∴AB

2

+BC

2

=AC

2

(Pythagoras theorem)

Hence, proved

∴ Δ ABC is a right triangle (proved)

Step-by-step explanation:

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