Exercise 3.2: Coordinate Geometry — NCERT Solutions

Take the corner post as the origin $(0,0)$, with 'right' along the positive x-axis and 'up' along the positive y-axis.

• 4 rows to the right → x-coordinate $= 4$
• 6 columns up → y-coordinate $= 6$

So the tree's position is $(4, 6)$.

Both coordinates are positive, so the tree lies in Quadrant I.

Take the centre as origin. Let east be positive x, west negative x; north be positive y.

Position P: 3 m east, 2 m north → $P(3, 2)$.

Position Q: 3 m west, 2 m north → $Q(-3, 2)$.

Observation: The two points have the same ordinate ($2$) but opposite abscissae ($3$ and $-3$). Therefore $P$ and $Q$ are mirror images of each other in the y-axis (they are equidistant from, and on opposite sides of, the y-axis).

(i) School $(2,3)$ and Market $(2,-1)$: they share the same abscissa ($x = 2$), so they lie on a vertical line. The distance is the difference of ordinates: $|3 - (-1)| = |3 + 1| = 4 \text{ units}$ In metres: $4 \times 100 = \mathbf{400\text{ m}}$.

(ii) School $(2,3)$ and Park $(-3,3)$: they share the same ordinate ($y = 3$), so they lie on a horizontal line. The distance is the difference of abscissae: $|2 - (-3)| = |2 + 3| = 5 \text{ units}$ In metres: $5 \times 100 = \mathbf{500\text{ m}}$.

Starting at harbour $O(0,0)$:

• $O(0,0) \to A(4,0)$: only x increases → sails 4 units east.
• $A(4,0) \to B(4,5)$: only y increases → sails 5 units north.
• $B(4,5) \to C(0,5)$: x decreases to 0 → sails 4 units west.
• $C(0,5) \to O(0,0)$: y decreases to 0 → sails 5 units south back to harbour.

The path traces a rectangle of length 4 units and breadth 5 units.

Point $B(4,5)$ has both coordinates positive, so it lies in Quadrant I.