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 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 9x-ky+7=0 is perpendicular to the line 2x-3y-3=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. Thanks from o2jam 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: 2,584 Thanks: 1430 I don't suppose you know your Prince do you? I've got a huge fortune I'm looking to invest. Thanks from jonah and Denis
 August 24th, 2018, 03:29 PM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 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
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Quote:
 Originally Posted by Harmeed 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 9x-ky+7=0 is perpendicular to the line 2x-3y-3=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.
I presume this was on some kind of assignment? If it takes you 14 days to solve them you need to consult with your instructors.

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 x-intercept (a, 0) and the y-intercept (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 2x-3y-3=0 as y=2/3x-1 so that it is in slope-intercept form. With that in mind, a slope perpendicular to that would be the opposite reciprocal -3/2x with the y-int or "b" in y=mx+b still being undefined. 2. I then rewrote the first line as yk= 9x-7. 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
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Quote:
 Originally Posted by Harmeed I know a lot of people are going to benefit from this.
Well, at least they'll have something to think about for maybe a minute or two, which would be ample time to obtain all the answers.

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