For the Assertion and Reason below, choose the correct alternative.

Assertion	Reason
The point $\mathrm{P} (5, -2)$  lies in the quadrant $\mathrm{IV}$	The signs of points in quadrants$\mathrm{I}, \mathrm{II}, \mathrm{III}$and $\mathrm{IV}$are respectively $(+, +), (-, +), (-, -)$and $(+, -)$
The point $\mathrm{O} (0, 2)$ lies on the $y$-axis	Every point on $y$-axis is of the form $(y, 0)$

During Durga Puja, a fair was held at Rita's village. It was held on the open football ground. Rita and her friends visited the fair. The whole fair was decorated with colourful lights. There were many stalls selling flowers, clothes, bangles, utensils, toys, fast food, sweets and ice cream, etc. There was a giant wheel, a small wheel, a merry-go-round and other jhoolas. Rita and her friends enjoyed the giant wheel and merry-go-round. They also ate fast food, sweets and ice creams. Rita bought some toys for her brother, utensils for her mother and bangles for herself. She returned to her home and plotted few stalls as points on a graph paper as shown below:

The distance between the Ice-cream stall and the Utensils stall is

You are lucky enough to have found the only surviving copy of a treasure map left by the notorious pirate Short James Platinum - scourge of the seven seas. He has buried many pieces of treasure on the island - each in different location.

The Tsarina's Tiara is buried due north of Kaspar's cave. It is as far from Kaspar's cave to the Tiara as it is from Mermaid Pool to Trader's Bay. The coordinates of the place where the Tsarina's Tiara is buried is

Ananya made a large trapezium by joining four equal trapeziums as shown in the figure.

Find the coordinates of the vertices of all these trapeziums.

Shown below is the seating arrangement in a classroom in $X-Y$ plane. The teacher’s position is the origin of $X-Y$ plane.

Pooja’s position is given as $\left(1, -1\right)$, then Ravi and Surya's position (respectively) are

You are lucky enough to have found the only surviving copy of a treasure map left by the notorious pirate Short James Platinum - scourge of the seven seas. He has buried many pieces of treasure on the island - each in different location.

Find the perpendicular distance of the place Skull Rock from the $x-$axis. 

Anmol loved to fly kites on Sankranti. He won a kite from the opponent and brought it with him to his home. He placed it on his big graph sheet such that the meeting point of the two diagonals was on the origin. He saw that it is in the shape of a Rhombus.

If the length of the longer diagonal was measured with scale and found to be $10 \mathrm{cm}$ and the shorter one was $8 \mathrm{cm}$, then find the coordinates of $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$.

If the co-ordinates of a point $\mathrm{M}\left(-2, 9\right)$ can also be expressed as $(1+x,y^2)$ where $y>0$, then find the quadrants in which the following points lie:

$\mathrm{P}(y, x), \mathrm{Q}(2, x), \mathrm{R}(x^2, y-1), \mathrm{S}(2x,-3y)$.