Section Formula

Q. If we draw a median AD in ∆ABC, are the altitudes of ∆ADB and ∆ADC equal in length? Justify.

Q. The coordinates of the third vertex of an equilateral triangle whose two vertices are at $(3,4),(-23)$ are ______.

1. $(1,7)$
2. $(5,1)$
3. $(\frac{1+\sqrt{3}}{2},\frac{7-5\sqrt{3}}{2})$ or $(\frac{1-\sqrt{3}}{2},\frac{7+5\sqrt{3}}{2})$
4. $(-5,5)$

Q.

The line $x+y=a$, meets the axis of $x$ and $y$ at $A$ and $B$ respectively. A triangle $AMN$ is inscribed in the triangle $OAB$, $O$ being the origin, with right angle at $N$, $M$ and $N$ lie respectively on $OB$ and $AB$. If the area of the triangle $AMN$ is $\frac{3}{8}$ of the area of the triangle $OAB$, then $\frac{AN}{BN}$ is equal to

1. 2

2. 3

3. $\frac{1}{3}$

4. $\frac{1}{2}$

Q. a, b, c are the sides of $△ABC$ such that a+b+c=2.,
find the max value of $a^2+b^2+c^2+2abc<2$

Q. For an equation to be balanced, the left hand side should be equal to the right hand side.

1. True
2. False

Q. If the points $A(0,3,p),B(-1,q,3),C(3,2,1)$ are collinear, then

1. C divides AB externally in ratio $1:3$
2. C divides AB internally in ratio $1:3$
3. C divides AB externally in ratio $3:1$
4. None of these