The hypotenuse of an isosceles right triangle has endpoints #(4,3)# and #(9,8)#. What is the length of one of the legs of the triangles?

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Answer 1 · 2018-03-12T17:59:21

# 5#.

Suppose that in the isosceles right- #DeltaABC, /_B=90^@#.

So #AC# is the hypotenuse, and we take, #A(4,3) & C(9,8)#.

Clearly, we have, #AB=BC..................(ast)#.

Applying Pythagoras Theorem, we have,

#AB^2+BC^2=AC^2=(4-9)^2+(3-8)^2#.

#:. BC^2+BC^2=25+25=50#.

#:. 2BC^2=50#.

#:. BC=sqrt(50/2)=sqrt25=5#.

# rArr AB=BC=5#.