Class 9th NCERT Math Solutions- Chapter 1 Orienting Yourself: The Use of Coordinates
Chapter Summary
Coordinate System: A structured grid framework used to define the exact physical location of points or objects using numbers.
Cartesian Plane (xy-plane): The two-dimensional surface divided by two intersecting perpendicular axes.
x-axis: The horizontal reference line on the coordinate plane.
y-axis: The vertical reference line on the coordinate plane.
Origin: The intersection point of the x-axis and y-axis, always denoted by the coordinates (0, 0).
Quadrants: The four distinct regions of the coordinate plane created by the intersection of the axes.
x-coordinate: The primary numerical value of a point, indicating its distance from the y-axis measured along the x-axis.
y-coordinate: The secondary numerical value of a point, indicating its distance from the x-axis measured along the y-axis.
Baudhāyana-Pythagoras Theorem: The fundamental geometric theorem utilized to calculate the exact distance between two points across the Cartesian plane.
Exercise 1.1 (Solutions)
Q.1 Fig. 1.3 shows Reiaan’s room with points OABC marking its corners. The x- and y-axes are marked in the figure. Point O is the origin. Referring to Fig. 1.3, answer the following questions:
(i) If D1R1 represents the door to Reiaan’s room, how far is the door from the left wall (the y-axis) of the room? How far is the door from the x-axis?
(ii) What are the coordinates of D1?
(iii) If R1 is the point (11.5, 0), how wide is the door? Do you think this is a comfortable width for the room door? If a person in a wheelchair wants to enter the room, will he/she be able to do so easily?
(iv) If B1 (0, 1.5) and B2 (0, 4) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?
Solution: (i) By observing the coordinate grid (Fig 1.3), the door starts at point D₁ on the x-axis. The x-coordinate of D₁ is 8. Therefore, the door is 8 units (or 8 ft) away from the left wall (y-axis). Since the door lies precisely on the x-axis, its distance from the x-axis is 0 units.
(ii) Point D₁ lies on the x-axis at a distance of 8 units from the origin. Thus, its coordinates are (8, 0).
(iii) Width Calculation: The width is the distance between R₁ and D₁.
Width = 11.5 – 8 = 3.5 ft.
Comfort & Accessibility: Yes, this is a very comfortable width. Standard room doors are usually around 3 ft wide. A standard wheelchair requires a minimum clear width of 32 inches (approx. 2.67 ft). At 3.5 ft, a person in a wheelchair will be able to enter easily.
(iv) Bathroom door width = y-coordinate of B₂ – y-coordinate of B₁ = 4 – 1.5 = 2.5 ft. Since 2.5 ft is less than 3.5 ft, the bathroom door is narrower than the room door.