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If the points (1, 3) and (5, 1) are two opposite vertices of a rectangle, and other two vertices lie on the line y = 2x + c, then find value of c.
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11 Answers
206@Astha
See, this is really simple
as it is mentioned other two vertices lie on the line y = 2x + c,
we can safely say that the mid- point of the other diagonal of the rectangle also lies on this line.....
So, use mid-point formula for the given points,
as this point lies on line y = 2x + c,
it satisfies the eqn....and you are done!! :)
Astha Gupta thanks sir....Upvote·0· Reply ·2013-06-08 23:14:28- Astha Gupta that was actually very simple....
101c=(-4)
- Sayantan Hazra Good work :)
- Sukrit Roy Chowdhury thnk u :)
- Astha Gupta hw did u get this...can u show..plzzz...
337But the line passing through the other two vertices do not have a slope 2. The slope is 0.5... ??? :(
- Sayan Sinha But the line passing through the other two vertices does not have a slope 2. The slope is 0.5... ??? :(
206Yes, the line passing through the other two vertices does have a slope 2......how is the slope 0.5 ????!!!????
337The other two vertices are (5,3) and (1,1). So,
y2-y1x2-x1 = 3-15-1 = 24 = 0.5
206How do you know the other two vertices are only (5,3) and (1,1) and not anything else?
337
It is clear from the image that the other two vertices are (5,3) and (1,1) .... Where am I going wrong....?
- Sayan Sinha The other two vertices are marked in green...
206it is nowhere mentioned in the question that the sides of the rectangle are parallel to the axes.......hence you have to assume a general rectangle which can be placed in any manner in the x-y plane.....
337Got it! Answer is -4....!
Interpretation of these CAT questions is what I need to pracice :P
Thanx a lot sir...
- Sayantan Hazra Was this a CAT question?? :O
I thought i just made it up ;)
337Another way.
If you see, the given slope for the other two vertices is 2. Compare the slope of the given vertices and you will find that the angle between the diagonals is 90°. Thus it is a square. (All squares are rectangles). So the sides are same. Equate them with x and y to find the equation...
- Astha Gupta i didn't undrstnd that hw did u determined the angles btwn d diagonals with the help of slope...can u xplain it....
thanku..
- Sayantan Hazra For perpendicular lines, product of their slopes is -1.....from given vertices, slope of diagonal formed by them is -0.5, and for given diagonal, slope = 2...product = -1.....
- Astha Gupta ya..i got it..!!!