Identify the correct statement-

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For option $(A)$: Let the line be $ax + by + c = 0$. The sum of perpendicular distances is $\frac{4a+2b+c}{\sqrt{a^2+b^2}} + \frac{2a+4b+c}{\sqrt{

Vedclass · Accepted Answer

If the algebraic sum of lengths of perpendiculars drawn from $(4,2)$,$(2,4)$,and the origin to a variable line is zero,then the line necessarily passes through $(2,2)$.

Vedclass · Answer

(A) For option $(A)$: Let the line be $ax + by + c = 0$. The sum of perpendicular distances is $\frac{4a+2b+c}{\sqrt{a^2+b^2}} + \frac{2a+4b+c}{\sqrt{a^2+b^2}} + \frac{c}{\sqrt{a^2+b^2}} = 0$. This implies $6a + 6b + 3c = 0$,or $2a + 2b + c = 0$. This is the condition for the line to pass through $(2,2)$. Thus,$(A)$ is true.For option $(B)$: The condition $Ar(\Delta PAB) + Ar(\Delta PBC) + Ar(\Delta PAC) = Ar(\Delta ABC)$ is satisfied for any point $P$ inside $\Delta ABC$,not just the orthocenter. Thus,$(B)$ is false.For option $(C)$: The angle bisectors of a pair of lines are perpendicular to each other,they do not bisect the angle between themselves. Thus,$(C)$ is false.For option $(D)$: The harmonic conjugate of the midpoint of $A$ and $B$ is at infinity. Thus,$(D)$ is false.

Similar Questions

$A(-2, 3)$ is a point on the line $4x + 3y - 1 = 0$. If the points on the line that are $10$ units away from the point $A$ are $(x_1, y_1)$ and $(x_2, y_2)$,then $(x_1 + y_1)^2 + (x_2 + y_2)^2 =$

The equation of the line passing through the intersection of $3x - 4y + 1 = 0$ and $5x + y - 1 = 0$ which cuts off equal intercepts on the axes is given by

The number of integral points (integral point means both the coordinates should be integers) exactly in the interior of the triangle with vertices $(0, 0)$,$(0, 21)$,and $(21, 0)$ is:

The number of integral values of $m$,for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is an integer,is:

The equation of the straight line in the normal form which is parallel to the lines $x+2y+3=0$ and $x+2y+8=0$ and divides the distance between these two lines in the ratio $1:2$ internally is

Vedclass Test Series

Exam Paper Generator

Online Exam Module