Chapter 5: Co-ordinate Geometry (Exercise 5.2)

Chapter 5: Co-ordinate Geometry (Exercise 5.2)

Question 1:
Plot the points A(1, 2), B(5, 2), C(5, 6), and D(1, 6) on a Cartesian plane. Join them in order A-B-C-D-A and name the geometrical figure obtained.

Solution:
* Distance AB = 5 - 1 = 4 units
* Distance BC = 6 - 2 = 4 units
* Distance CD = 5 - 1 = 4 units
* Distance DA = 6 - 2 = 4 units

* Since all four sides are equal and all interior angles are 90°, the geometrical figure formed is a Square.

Question 2:
Plot the points P(-3, 2), Q(3, 2), and R(0, -3) on a coordinate plane. Join P to Q, Q to R, and R to P. Name the polygon formed.

Solution:
* Joining the points P, Q, and R forms a closed 3-sided polygon.
* Side length PQ = 3 - (-3) = 6 units.
* Distance PR = √[(0 - (-3))² + (-3 - 2)²] = √(9 + 25) = √34 units.
* Distance QR = √[(0 - 3)² + (-3 - 2)²] = √(9 + 25) = √34 units.

* Since PR = QR, the polygon formed is an Isosceles Triangle.

Question 3:
Find the perpendicular distance of the point P(4, 5) from:
1. The X-axis
2. The Y-axis

Solution:
For any point (x, y) in the Cartesian plane:
1. The perpendicular distance from the X-axis is equal to the absolute value of the Y-coordinate (Ordinate) = 5 units.
2. The perpendicular distance from the Y-axis is equal to the absolute value of the X-coordinate (Abscissa) = 4 units.

Question 4:
Without plotting the points on a graph paper, state the quadrant or axis in which each of the following points lies:
1. (0, -4)
2. (-5, -2)
3. (7, 0)
4. (-3, 8)

Solution:
1. (0, -4): Since X-coordinate is 0, the point lies on the Negative Y-axis.
2. (-5, -2): Both X and Y coordinates are negative, so it lies in Quadrant III.
3. (7, 0): Since Y-coordinate is 0, the point lies on the Positive X-axis.
4. (-3, 8): X-coordinate is negative and Y-coordinate is positive, so it lies in Quadrant II.