#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# 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 AKASH GOYAL AskiitiansExpert-IITD
419 Points
11 years ago

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

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.

11 years ago

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

4 years ago
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
one year ago
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 = – 4
So, 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)
∴ Slope of AD × Slope of AB = – 1.

When x1 = 4 and x2 = 2, we get
Coordinates 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 get
Coordinates 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).