August 24th, 2018, 01:46 PM  #1 
Member Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2  Geometry challenging questions
Yeah......As the title implies, you are about to witness the top 3 plane geometry questions which took me days to solve... So are you ready? Because these questions are for professional Geometry genius.... 1. The line 9xky+7=0 is perpendicular to the line 2x3y3=0. Find the value of constant k. 2. If the points (3,1), (2,k) and (7,3) are collinear, where k is constant, find the value of k. 3. A straight line passes through the point (2,3) and makes equal intercepts on the x and y axes. Find its equation. I see you've started shaking already, but for those who are confident of themselves, they will solve it. It took me 14 days to puzzle out the solution as a 9th grader... Note: WHEN SOLVING, SHOW ALL WORKINGS CAREFULLY. All question are genuine and confirmed. May your knowledge increase as you solve and show all working carefully. I know a lot of people are going to benefit from this. Last edited by skipjack; August 25th, 2018 at 06:48 AM. 
August 24th, 2018, 02:38 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 
I don't suppose you know your Prince do you? I've got a huge fortune I'm looking to invest.

August 24th, 2018, 03:29 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
IF you've solved them, WHY do you want to see how others do it? Looks like you're looking for a solution! 
August 24th, 2018, 03:40 PM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,257 Thanks: 928 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Hints: 1. The slope of two perpendicular lines are negative inverses. ie. m2 = 1/m1. 2. Find the slope of the line from the points (3, 1) and (7, 3). Since all points are on the same line this will also be the slope between the points (3, 1) and (2, k). 3. Call the xintercept (a, 0) and the yintercept (0, b). Now, as in 2, you have a line with the three points (a, 0), (0, b), and (2, 3). Compute the slopes as in problem 2 and you'll get two equations in two unknowns. Dan Last edited by skipjack; August 25th, 2018 at 06:49 AM.  
August 24th, 2018, 03:42 PM  #5 
Newbie Joined: Aug 2018 From: PA Posts: 2 Thanks: 0 Math Focus: geometry 
I worked out the answer to be 6 for the first problem regarding the value k. 1. I rewrote 2x3y3=0 as y=2/3x1 so that it is in slopeintercept form. With that in mind, a slope perpendicular to that would be the opposite reciprocal 3/2x with the yint or "b" in y=mx+b still being undefined. 2. I then rewrote the first line as yk= 9x7. To get 9x to simplify to 3/2x, I set k as 6 and divided in the equation to get 3/2x. Please correct me if I'm wrong. I would like to know the answer if this is not it. Last edited by skipjack; August 25th, 2018 at 06:40 AM. 
August 25th, 2018, 06:59 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203  

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