Question

For what value of 'x' are A(2,3), B(x,y) and C(4,3) the vertices of a right triangle with right angle a A? ​

Answer 1

Answer:

Given A(4,3),B(−1,y) and C(3,4)

AB2+AC2=BC2

AB2=(4+1)2+(3−y)2

=25+(3−y)2

AC2=(4−3)2+(3−4)2

=1+1=2

BC2=(−1−3)2+(y−4)2

=16+(y−4)2

∴25+(3−y)2+2=16+(y−4)2

25+9−6y+y2+2=16+y2−8y+16

2y=−4

y=−2

Answer 2

Answer:

Given A(4,3),B(−1,y) and C(3,4)

AB2+AC2=BC2

AB2=(4+1)2+(3−y)2

=25+(3−y)2

AC2=(4−3)2+(3−4)2

=1+1=2

BC2=(−1−3)2+(y−4)2

=16+(y−4)2

∴25+(3−y)2+2=16+(y−4)2

25+9−6y+y2+2=16+y2−8y+16

2y=−4

y=−2

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Step-by-step explanation: