in Quantitative Aptitude recategorized by
416 views
1 vote
1 vote

Two opposite vertices of a rectangle are $(1,3)$ and $(5,1)$ while the other two vertices lie on the straight line $y=2x+c$. Then the value of $c$ is

  1. $4$
  2. $3$
  3. $-4$
  4. $-3$
in Quantitative Aptitude recategorized by
by
416 views

1 Answer

0 votes
0 votes

Answer $C$

$\because $ We know that the diagonals of the $RECTANGLE$ bisect each other.

So, equation of the diagonal must be satisfied by the mid-points of the diagonal.

Now, mid-points of diagonal can be calculated by the mid-point formula as:

$\bigg (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\bigg ) =\bigg ( \frac{1+5}{2}, \frac{3+1}{2}\bigg ) = (3, 2)$

The equation of the diagonal is given as:

$$ y = 2x + c$$

Substitute the values of $x$, and $y$ coordinates, we get:

$$2 = 2 \times 3 + c \Rightarrow \color {blue}{c = -4}$$

$\therefore \;C$ is the correct option.

edited by
by

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true