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If the sides of a right angled triangle are represented by the lines x

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Senior Manager
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Joined: 25 Dec 2018
Posts: 485
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
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If the sides of a right angled triangle are represented by the lines x  [#permalink]

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New post 05 Mar 2019, 07:25
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Difficulty:

  65% (hard)

Question Stats:

35% (02:14) correct 65% (02:25) wrong based on 17 sessions

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If the sides of a right angled triangle are represented by the lines x + y − 8 =0 , 3x − 2y + 1 = 0 and x − y = 0, then the vertex opposite to the hypotenuse is given by?

A. (3,5)
B. (0,0)
C. (4,4)
D. (−1,−1)
E. None of these
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Re: If the sides of a right angled triangle are represented by the lines x  [#permalink]

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New post 06 Mar 2019, 00:13
1
mangamma wrote:
If the sides of a right angled triangle are represented by the lines x + y − 8 =0 , 3x − 2y + 1 = 0 and x − y = 0, then the vertex opposite to the hypotenuse is given by?

A. (3,5)
B. (0,0)
C. (4,4)
D. (−1,−1)
E. None of these


We have to find out the slope of the lines first.

1) x + y − 8 =0 ; slope=m1=-1
2) 3x − 2y + 1 = 0; slope=m2=3/2
3) x − y = 0; slope=m3=1

Since the triangle is a right angled one, hence two lines must be perpendicular to each other and the intersection of these two lines shall be the vertex opposite the hypotenuse.

See that m1*m3=-1

Hence , the intersection of the line x + y − 8 =0 & x − y = 0 is the required vertex.

Upon solving the above two equations, we have x=y=4

Ans. (C)
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Re: If the sides of a right angled triangle are represented by the lines x  [#permalink]

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New post 15 May 2019, 18:15
1
Hi,
General slope form of a line ax+by+c=0 is:- y=mx+c, where 'm' is the slope.

Given line x+y-8=0.Now transforming the line into its slope form, y=-x+8 or y=(-1)x+8.
Now comparing this equation with the general slope form, we have m=slope=-1.

Similarly, obtain slope the slope of the other two equations.

Hope it helps.

Posted from my mobile device
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PKN

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Re: If the sides of a right angled triangle are represented by the lines x   [#permalink] 15 May 2019, 18:15
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