NCERT Solutions Class 7 Maths Chapter 13 — Coordinate Geometry Introduction

Solution:

Step 1: The Cartesian plane is formed by two perpendicular number lines: the horizontal x-axis and the vertical y-axis.

Step 2: These two axes intersect at a point called the origin, which has coordinates (0, 0).

Step 3: Therefore, the statement that the x-axis is horizontal, the y-axis is vertical, and they intersect at the origin is correct.

Solution:

Step 1: The origin is the point where the x-axis and the y-axis intersect.

Step 2: At this intersection point, the value on the x-axis is 0, and the value on the y-axis is 0.

Step 3: Thus, the coordinates of the origin are (0, 0).

Solution:

Step 1: In an ordered pair (x, y), the first number (x) always represents the position along the x-axis, and the second number (y) always represents the position along the y-axis.

Step 2: If you swap the order, for example, (3, 5) versus (5, 3), these represent two completely different points on the coordinate plane.

Step 3: Therefore, 'ordered' signifies that the sequence of numbers is crucial for defining the point's unique location.

Solution:

Step 1: For a point (x, y), the x-coordinate indicates horizontal movement from the origin, and the y-coordinate indicates vertical movement.

Step 2: A positive x-coordinate (like 4) means moving 4 units to the right. A negative y-coordinate (like -2) means moving 2 units down.

Step 3: Ravi incorrectly started by moving down (y-axis) and then right (x-axis), and also assigned the negative sign to the wrong coordinate during his movement description.

Step 4: The correct method is to move 4 units right (for x=4) and then 2 units down (for y=-2).

Solution:

Step 1: The x-coordinate describes the horizontal position relative to the y-axis. '5 units to the left of the y-axis' means x = -5.

Step 2: The y-coordinate describes the vertical position relative to the x-axis. '3 units above the x-axis' means y = 3.

Step 3: Combining these, the coordinates of point M are (-5, 3).