recategorized by
421 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

Related questions

0 votes
0 votes
1 answer
1
Arjun asked Sep 23, 2019
370 views
If $a,b,c$ are sides of a triangle $ABC$ such that $x^2-2(a+b+c)x+3 \lambda (ab+bc+ca)=0$ has real roots then$\lambda < \frac{4}{3}$$\lambda \frac{5}{3}$$\lambda \in \bi...
2 votes
2 votes
1 answer
2
1 votes
1 votes
1 answer
3
0 votes
0 votes
1 answer
4
gatecse asked Sep 18, 2019
331 views
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2), (3,-4)$ and $(5,6)$ is$12$$14$$16$$18$