Question

The points (1, 3) and (5, 1) are two opposite vert of a rectangle. The other two vertices lie on the line find the `y=2x+c`. Find `c` and the remaining vertices.
A. 2
B. `-2`
C. 4
D. `-4`

Answer 1

Correct Answer - D
Given, opposite vertices of rectangle are A(1. 3) and C(5, 1)
We know, diagonals fo rectangle bisect each other. So, midpoint of AC lies on line `y=2x+c`.
Mid point of `AC= ((1+5)/2, (3+1)/2)=(6/2, 4/2)=(3, 2)`
`y=2x+c implies 2=2(3)+c`
`implies c=2-6=-4`