If the perpendicular bisector of the line seg | vedclass

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

Question

(D) The midpoint $M$ of the line segment $PQ$ is given by $M = \left(\frac{1+k}{2}, \frac{4+3}{2}\right) = \left(\frac{k+1}{2}, \frac{7}{2}\right)$.Th

Vedclass · Accepted Answer

$-4$

Vedclass · Answer

(D) The midpoint $M$ of the line segment $PQ$ is given by $M = \left(\frac{1+k}{2}, \frac{4+3}{2}\right) = \left(\frac{k+1}{2}, \frac{7}{2}\right)$.The slope of the line segment $PQ$ is $m_{PQ} = \frac{3-4}{k-1} = \frac{-1}{k-1}$.The slope of the perpendicular bisector is $m = -\frac{1}{m_{PQ}} = k-1$.The equation of the perpendicular bisector passing through $M$ with slope $m$ is $y - \frac{7}{2} = (k-1)\left(x - \frac{k+1}{2}\right)$.The $y$-intercept is the value of $y$ when $x=0$. Given the $y$-intercept is $-4$,we substitute $x=0$ and $y=-4$ into the equation:$-4 - \frac{7}{2} = (k-1)\left(0 - \frac{k+1}{2}\right)$$-\frac{15}{2} = (k-1)\left(-\frac{k+1}{2}\right)$$\frac{15}{2} = \frac{(k-1)(k+1)}{2}$$15 = k^2 - 1$$k^2 = 16$$k = \pm 4$.Since $-4$ is an option,the correct value is $-4$.

If the perpendicular bisector of the line segment joining the points $P(1, 4)$ and $Q(k, 3)$ has a $y$-intercept equal to $-4$,then a value of $k$ is

Similar Questions

The equations of the perpendicular bisectors of the sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y+5=0$,respectively. If $A$ is $(1, -2)$,then the equation of the straight line $BC$ is

The equation of the line bisecting the line segment joining the points $(a, b)$ and $(a', b')$ at a right angle is

Find the equation of a line which passes through $(2 \cos^3 \theta, 2 \sin^3 \theta)$ and is perpendicular to the line $x \cos \theta - y \sin \theta = 2 \cos 2 \theta$.

The equation of the straight line which passes through the point $(a \cos^{3} \theta, a \sin^{3} \theta)$ and is perpendicular to $x \sec \theta + y \operatorname{cosec} \theta = a$ is

The equation of the line bisecting perpendicularly the segment joining the points $(-4, 6)$ and $(8, 8)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module