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# Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If l

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If l  [#permalink]

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04 Oct 2018, 00:58
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Difficulty:

55% (hard)

Question Stats:

55% (01:38) correct 45% (02:11) wrong based on 42 sessions

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[Math Revolution GMAT math practice question]

Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If lines AB and BC are perpendicular to each other, p=?

A. -2
B. -1
C. 0
D. 1
E. 2

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself"  Math Revolution Discount Codes EMPOWERgmat Discount Codes Optimus Prep Discount Codes Intern Joined: 17 Mar 2018 Posts: 37 Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If l [#permalink] ### Show Tags 04 Oct 2018, 01:20 1 MathRevolution wrote: [Math Revolution GMAT math practice question] Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If lines AB and BC are perpendicular to each other, p=? A. -2 B. -1 C. 0 D. 1 E. 2 Perpendicular bisectors have a negative reciprocal of their slopes. A (1,4) B (2,2) C (p,1) Slope of AB= 4-2/1-2=-2 Slope of BC will be 1/2 or slope of BC= 2-1/2-p=1/2---- cross multiply (2-1)2=2-p 4-2=2-p 4-2-2=p 0=p Therefore p=0 GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 365 Re: Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If l [#permalink] ### Show Tags 04 Oct 2018, 07:05 MathRevolution wrote: [Math Revolution GMAT math practice question] Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If lines AB and BC are perpendicular to each other, p=? A. -2 B. -1 C. 0 D. 1 E. 2 Line AB is oblique (non-horizontal and non-vertical) therefore line BC is also oblique, and the product of their slopes must be -1. $$?\,\, = \,p$$ $${\text{slope}}{\,_{\overleftrightarrow {{\text{AB}}}}}\,\, = \,\,\,\frac{{4 - 2}}{{1 - 2}}\,\, = \, - 2\,$$ $$\frac{1}{2}\,\,{\text{ = }}\,\,{\text{slope}}{\,_{\overleftrightarrow {{\text{BC}}}}}\,\,\,\,{\text{ = }}\,\,\frac{{2 - 1}}{{2 - p}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,p = 0$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT) Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6371 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If l [#permalink] ### Show Tags 07 Oct 2018, 18:37 => The slope of the line segment joining the two points (x1,y1) and (x2,y2) is (y1-y2)/(x1-x2). The product of the slopes of perpendicular lines is $$-1$$. The slope of the line AB is $$\frac{(4-2)}{(1-2)} = -2.$$ Since the two lines AB and BC are perpendicular each other, the slope of BC, which is $$\frac{(2-1)}{(2-p)}$$, must be $$\frac{1}{2}.$$ So, $$\frac{(2-1)}{(2-p)}=\frac{1}{2}$$ $$\frac{1}{(2-p)}=\frac{1}{2}.$$ Thus, $$2 – p = 2$$, and $$p = 0$$. Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If l &nbs [#permalink] 07 Oct 2018, 18:37
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