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

Question

AKASH GOYAL AskiitiansExpert-IITD · Answer

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..

vikas askiitian expert · Answer

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

Bhaskar Tiwari · Answer

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

ankit singh · Answer

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) AD ⊥ AB, ∴ 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).

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

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

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

4 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Analytical Geometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship