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Two points (a,3) and (5,b) are the opposite vertices of a rectangle.If the other two...
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We know that the diagonal of the rectangle intercepts at the mid point of each diagonal as well as mid point of triangle.
If the mid point is M (p,q) then using points (a,3) and (5,b);
`p = (a+5)/2`
`q = (3+b)/2`
This point M is on `y = 2x+c.`
`(3+b)/2 = 2(a+5)/2+c`
`3+b = 2(a+5)+2c`
`b-2a = 7+2c-----(1)`
Point `(a/c,b/c)` is also on the line `y = 2x+c.`
`b/c = 2xxa/c+c`
`b-2a = c^2 ----(2)`
`(1) = (2)`
`7+2c = c^2`
`c^2-2c-7 = 0`
Solving the quadratic equation will give you;
`c = (2+-sqrt(4+4xx1xx7))/(2xx1)`
`c = (2+-4sqrt2)/2 = 1+-2sqrt2`
So possible answers for c are;
`c = 1+2sqrt2`
`c = 1-2sqrt2`
Correct answer is C.
Posted by jeew-m on June 20, 2013 at 7:47 PM (Answer #1)
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