Suppose A and B are two points on the line 2x | vedclass

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

Question

(A) Let $M$ be the mid-point of $AB$. Since $PA=PB$,the triangle $PAB$ is an isosceles triangle with $PA=PB$. In an isosceles triangle,the median from

Vedclass · Accepted Answer

$\left(\frac{-1}{5}, \frac{13}{5}\right)$

Vedclass · Answer

(A) Let $M$ be the mid-point of $AB$. Since $PA=PB$,the triangle $PAB$ is an isosceles triangle with $PA=PB$. In an isosceles triangle,the median from the vertex $P$ to the base $AB$ is also the altitude to the base $AB$. Thus,$PM \perp AB$. The slope of the line $AB$ (which is $2x-y+3=0$ or $y=2x+3$) is $m_1 = 2$. Since $PM \perp AB$,the slope of $PM$ is $m_2 = -\frac{1}{m_1} = -\frac{1}{2}$. The line $PM$ passes through $P(1,2)$ and has a slope of $-\frac{1}{2}$. The equation of line $PM$ is $y-2 = -\frac{1}{2}(x-1)$,which simplifies to $2y-4 = -x+1$,or $x+2y-5=0$. The mid-point $M$ is the intersection of the lines $2x-y+3=0$ and $x+2y-5=0$. From the first equation,$y=2x+3$. Substituting this into the second equation: $x+2(2x+3)-5=0 $ $\Rightarrow x+4x+6-5=0 $ $\Rightarrow 5x+1=0 $ $\Rightarrow x = -\frac{1}{5}$. Now,$y = 2(-\frac{1}{5})+3 = -\frac{2}{5}+3 = \frac{13}{5}$. Thus,the mid-point $M$ is $\left(-\frac{1}{5}, \frac{13}{5}\right)$.

Suppose $A$ and $B$ are two points on the line $2x-y+3=0$ and $P(1,2)$ is a point such that $PA=PB$. Then,the mid-point of $AB$ is

Similar Questions

The number of structural isomers for $C_6H_{14}$ is

$\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{14-6 \sqrt{5}}}}$ is equal to

The atomic weight of an element is $39$. The number of neutrons in its nucleus is one more than the number of protons. The number of protons,neutrons and electrons respectively in its atom would be

Which of the following is $NOT$ a characteristic of Phylum $Annelida$?

An $AC$ voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $\omega$ is increased:

Vedclass Test Series

Exam Paper Generator

Online Exam Module