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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Points J (3, 1) and K (-1, -3) are two vertices of an... tagged by: AAPL ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Points J (3, 1) and K (-1, -3) are two vertices of an... Points J (3, 1) and K ( -1, -3) are two vertices of an isosceles triangle. If L is the third vertex and has a y-coordinate of 6, what is the x-coordinate of L? A. -3 B. -4 C. -5 D. -6 E. -7 The OA is D. I don't have clear this PS question. Can I determine the x-coordinate value of L using the expression? $$d\left(P_1,P_2\right)=\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$ distance between 2 points in the coordinate plane. Where P1 and P2 can be, P1 (J or K) and P2 (L) I appreciate if any expert explain it for me. Thank you so much. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello AAPL. Let's take a look at your question. You are right. We have to use the formula $$d\left(P_1,P_2\right)=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}.$$ We have that J=(3,1), K=(-1,-3) and L=(x,6). Then $$d\left(J,\ L\right)=\sqrt{\left(x-3\right)^2+\left(6-1\right)^2}=\sqrt{\left(x-3\right)^2+25}$$ $$d\left(K\ ,\ L\right)=\sqrt{\left(x+1\right)^2+\left(6+3\right)^2}=\sqrt{\left(x+1\right)^2+81}$$ and $$d\left(J,\ K\right)=\sqrt{\left(-1-3\right)^2+\left(-3-1\right)^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}.$$ Now, since the triangle is isosceles, we have that $$d\left(J,\ L\right)=d\left(K,\ L\right)\ \Leftrightarrow\ \ \ \sqrt{\left(x-3\right)^2+25}=\sqrt{\left(x+1\right)^2+81}$$ $$\Leftrightarrow\ \left(x-3\right)^2+25\ =\ \left(x+1\right)^2+81\$$ $$\Leftrightarrow x^2-6x+9+25\ =\ x^2+2x+1+81$$ $$\Leftrightarrow\ -8x=48$$ $$\Leftrightarrow\ x=-6.$$ This is why the correct answer is the option D=-6. I hope this explanation may help you. I'm available if you'd like a follow-up. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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