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The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a  right traingle ,right-angled at B. Find the values of p. - CBSE Class 10 - Mathematics

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Question

The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a  right traingle ,right-angled at B. Find the values of p.

Solution

ΔABC is right triangle at B.

AC2+ AB2= BC2 ....(1)

Also, A=( 4,7) , B=( p,3) and C=( 7,3)

Now, AC2=97-4)2+(3-7_2=(3)2+(-4)2=9+16=25

AB2=(p-4)2+(3-7)2=p2-8p+16+(-4)2

=p2-8p+16+16

=p2-8p+32

ΔABC is right triangle at B.

AC2+ AB2= BC2 ....(1)

Also, A=( 4,7) , B=( p,3) and C=( 7,3)

Now, AC2=(7-4)2+(3-7)2=(3)2+(-4)2=9+16=25

AB2=(p-4)2+(3-7)2=p2-8p+16+(-4)2

=p2-8p+16+16

=p2-8p+32

BC2=(7-p)2+(3-3)2=49-14p+p2+0

=p2-14p+49

bc2=(7-p)2+(3-3)2=49-14p+p2+0

=p2-14p+49

From (1), we have

25= (p2- 8p +32)+( p2-14p+49)

25=2p2-22p+81

2p2-22p+56=0

p2-11p+28=0

p2-7p-4p+28=0

(p-4)(p-7)=0

p=4,p=7

  Is there an error in this question or solution?
Solution The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a  right traingle ,right-angled at B. Find the values of p. Concept: Pythagoras Theorem.
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