Find the values of a for which the triangle Δ A B C is an isosceles triangle, where A , B , and C have the coordinates ( − 1 , 1 ) , ( 1 , 3 ) , and ( 3 , a ) respectively.
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ABC is an isosceles triangl...
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Asked on December 20, 2019 by
Amardeep Mech
ABC is an isosceles triangle. If the coordinates of the base are B(1,3) and C(−2,7), the coordinates of vertex A can be
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AB=AC
(x−1)
2
+(y−3)
2
=
(x−(−2))
2
+(y−7)
2
(x−1)
2
+(y−3)
2
=(x+2)
2
+(y−7)
2
=2x+1−6y+9=4x+4−14y+49
⇒6x−8y+43=0
By substituting (
6
5
,6)
⇒
6×
6
5
−8×6+43
⇒0
Hence (
6
5
,6) is answer.
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