R. D. Sharma Solutions for Chapter: Co-Ordinate Geometry, Exercise 6: VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

If $\mathrm{A}(1,2), \mathrm{B}(4,3)$ and $\mathrm{C}(6,6)$ are the three vertices of a parallelogram $\mathrm{ABCD}$. If the coordinates of $\mathrm{D}$ are $\left(\mathrm{x},\mathrm{y}\right)$, then find the value of $\left(\mathrm{x}+\mathrm{y}\right)$.

What is the distance between the points $A\left(\sin \theta -\cos \theta ,0\right)$ and $B\left(0,\sin \theta +\cos \theta \right)$? If the distance is $d$, and $d^2=m,$then write the value of $m$ only?

Coordinates of the point where the perpendicular bisector of the line segment joining the points $\mathrm{A}(1,5)$, and $\mathrm{B}(4,6)$ cuts the $y$-axis is $\left(x,y\right)$. If $x+y=m$, then write the value of $m$.

If the area of a triangle with vertices $(\mathrm{a},\mathrm{b}+\mathrm{c}), (\mathrm{b},\mathrm{c}+\mathrm{a})$ and $(\mathrm{c},\mathrm{a}+\mathrm{b})$ is $\mathrm{k}$ square units, then find the value of $\mathrm{k}$.

The points $A(1,2), O(0,0)$ and $C(a,b)$ are collinear. If $a:b=k:2$, then find the value of $k$.

If the $\mathrm{x}$-coordinate of a point, which is equidistant from the three vertices $\mathrm{A}(2\mathrm{x}, 0), \mathrm{O}(0, 0)$ and $\mathrm{B}(0, 2\mathrm{y})$ of $△\mathrm{AOB}$ is $\mathrm{y}$, find the sum of the coordinates of point.

The distance between the points $(4, \mathrm{k})$ and $(1,0)$ is $5$. If the possible values of $k$ is $\pm A$ then find the value of $A$.

Find the distance of a point $\mathrm{P}(x, y)$ from the origin. The distance is denoted by $d$ and $d^2$ is obtained as the sum of variables $x \text{and} y$ having power represented by $n$, what is the value of $n?$