The vertices of a triangle are A(2, a), B(-3, 1) and C(-8, -2) right-angled at A. Find the possible values of a.

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asked Aug 15, 2022 33.0k views

5 votes

The vertices of a triangle are A(2, a), B(-3, 1) and C(-8, -2) right-angled at A. Find the possible values of a.

Mathematics
college

NealB asked

by NealB

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1 Answer

3 votes

Answer:

$BC = √((-3+8)^2 +(1+2)^2) = √(34)\\\\AB =√((-3-2)^2+(1-a)^2) = √(25+(1-a)^2) \\\\AC = √((2+8)^2+(a+2)^2) = √(100+(a+2)^2) \\\\AB^2 + AC^2 = BC^2\\\\ (√(25+(1-a)^2))^2+ (√(100+(a+2)^2))^2= (√(34))^2 \\\\25+(1-a)^2+100+(a+2)^2=34\\\\125+1+a^2-2a+a^2+4+2a=34\\\\130+2a^2 =34\\\\2a^2+96=0\\\\a^2+48=0\\\\a = √(-48)$