Revision sem1 q6

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.

11 Answers

206
Sayantan Hazra ·

@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!! :)

101
Sukrit Roy Chowdhury ·

c=(-4)

337
Sayan Sinha ·

12

337
Sayan Sinha ·

But the line passing through the other two vertices do not have a slope 2. The slope is 0.5... ??? :(

206
Sayantan Hazra ·

Yes, the line passing through the other two vertices does have a slope 2......how is the slope 0.5 ????!!!????

337
Sayan Sinha ·

The other two vertices are (5,3) and (1,1). So,
y2-y1x2-x1 = 3-15-1 = 24 = 0.5

206
Sayantan Hazra ·

How do you know the other two vertices are only (5,3) and (1,1) and not anything else?

337
Sayan Sinha ·

It is clear from the image that the other two vertices are (5,3) and (1,1) .... Where am I going wrong....?

206
Sayantan Hazra ·

it 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.....

337
Sayan Sinha ·

Got it! Answer is -4....!

Interpretation of these CAT questions is what I need to pracice :P
Thanx a lot sir...

337
Sayan Sinha ·

Another 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...

Your Answer

Close [X]