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Question

If A(4,3), B(-1,y) and C(3,4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.

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Solution


Given the triangle ABC,right angled at A.

Now, AB=(x2x1)2+(y2y1)2

AB=(14)2+(y3)2

AB=(5)2+(y3)2

AB=25+(y3)2

AB=25+y2+96y

AB=34+y26y

BC=(3(1))2+(4y)2

BC=(4)2+(4y)2

BC=16+16+y28y

BC=32+y28y

AC=(34)2+(43)2

AC=(1)2+(1)2

AC=1+1

AC=2 units

Given, ABC is a right angled triangle, right angled at A

So,by Pythagoras theorem BC2=AC2+AB2

(32+y28y)2=(2)2+(32+y26y)2

32+y28y=2+34+y26y

-2y=4

y=-2

Hence,the value of y is -2.


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