If point A(7,k) is the vertex of an isosceles triangle ABC with base BC, where B=(2,4) and C=(6,10), then what is k?

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May 14, 2017

Answer:

#k=5#

Explanation:

An isosceles triangle is a triangle with at least two equal sides. In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The vertex opposite the base is called the apex.

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Given #BC# is the base and #A(7,k)# is the apex, #=> AB and AC# are the two equal sides.
#=> AB=AC#
#=> sqrt((2-7)^2+(4-k)^2)=sqrt((6-7)^2+(10-k)^2)#
#=> (2-7)^2+(4-k)^2=(6-7)^2+(10-k)^2#
#=> 25+16-8k+cancel(k^2)=1+100-20k+cancel(k^2)#
#=> 25+16-8k=1+100-20k#
#=> -8k+20k=1+100-25-16#
#=> 12k=60#
#=> k=60/12=5#

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