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if the pts (1,3) and (5,1) are two opposite vertices of a rectangle and the other two vertices lie on the line Y=2X+C, then the value of c is
Dear Deva diagonals of rectangle bisect each other.let ABCD is rectangle. and A=(1,3), C=(5,1) Mid point of diagonal AC is (3,2) mid point of diagonal BD will also be (3,2) and given line is equation of BD (3,2) will satisfy the equation put y=2 and x=3 2=6+c c=-4 All the best. AKASH GOYAL AskiitiansExpert-IITD Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
Dear Deva
diagonals of rectangle bisect each other.let ABCD is rectangle. and A=(1,3), C=(5,1)
Mid point of diagonal AC is (3,2)
mid point of diagonal BD will also be (3,2) and given line is equation of BD
(3,2) will satisfy the equation
put y=2 and x=3
2=6+c
c=-4
All the best.
AKASH GOYAL
AskiitiansExpert-IITD
Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
LET ABCD is the rectangle let A,C are (1,3) , (5,1) then mid point of line AC is (3,2) now mid point of line BD is same so line passing through B,D will pass mid point & (3,2) will satisfy the equation of line.. Y = 2X+C at (3,2) 2 = 3*2 + C C= -4
Diagonals bisectors each other so mid point of given diagonal would also be mid point of other i.e, lies on equation and would satisfy so we get close =, - 4 on putting the point on line
ABCD is a rectangular.Let A(1, 3), B(x1, y1), C(5, 1) and D(x2, y2) be the vertices of the rectangular.We know that, diagonals of rectangular bisect each other.Let O be the point of intersection of diagonal AC and BD.∴ Mid point of AC = Mid point BD. Now, O(3, 2) lies on y = 2x + c.∴ 2 = 2 × 3 + c⇒ c = 2 – 6 = – 4So, the value of c is – 4.(x1, y1) lies on y = 2x – 4.∴ y1 = 2x1 – 4 ...(2)(x2, y2) lies on y = 2x – 4∴ y2 = 2x2 – 4 ...(3)Coordinates of B = (x1, 2x1 – 4)Coordinates of D = (x2, 2x2 – 4)AD ⊥ AB,∴ Slope of AD × Slope of AB = – 1. When x1 = 4 and x2 = 2, we getCoordinates of B = (x1, 2x1 – 4) = (4, 2 × 4 – 4) = (4, 4)Coordinates of D = (x2, 2x2 – 4) = (2, 2 × 2 – 4) = (2, 0)When x1 = 2 and x2 = 4, we getCoordinates of B = (x1, 2x1– 4) = (4, 2 × 4 – 4) = (2, 0)Coordinates of D = (x2, 2x2 – 4) = (4, 2 × 4 – 4) = (4, 4)Thus, the other two vertices of the rectangle are (2, 0) and (4, 4).
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