. Show that points A(7, 5), B(2, 3) and C(6, -7) are the vertices of a right triangle. Also find it's area *
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Step-by-step explanation:
Given points are
A(7,5),B(2,3),C(6,-7)
By distance formula
AB =√(3-5)^2+(2-7)^2
=√(-2)^2+(-5)^2
=√4+25
=√29
BC =√(-7-3)^2+(6-2)^2
=√100+16
=√116
AC = √(-7-5)^2+(6-7)^2
=√145
Pythagoras Theron
AC^2=BC^2+AB^2
(√145)^2= (√116)^2+(√29)^2
145=116+29
145=145
LHS = RHS
therefore the given vertices are if right angled triangle
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