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,

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

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

$:. 2BC^2=50$ .

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

$rArr AB=BC=5$ .

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