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Sameer claims that (−6, 1) is nearer to the -axis than (−1, 8), because −6 is smaller than −1. Is he right?

Class 9Coordinate GeometryCoordinate Geometry
  • AYes, because −6 is smaller than −1.
  • BYes, because the point with the more negative abscissa is always nearer the -axis.
  • CNo — both points are the same distance from the -axis.
  • DNo — distance from the -axis is the size of the abscissa, so (−1, 8) is 1 unit away and (−6, 1) is 6 units away.

Step-by-Step Solution

A distance is measured without a sign. The abscissae give distances of 1 unit and 6 units, so (−1, 8) is the nearer point. Comparing the signed values −6 < −1 is not the same as comparing distances.
Answer: D) No — distance from the -axis is the size of the abscissa, so (−1, 8) is 1 unit away and (−6, 1) is 6 units away.

Key idea: The Cartesian plane

Two perpendicular axes — horizontal -axis) and vertical -axis) — meet at the **origin** (0, 0). Together they divide the plane into four **quadrants**:

- **I**: > 0 (top right)
- **II**: > 0 (top left)
- **III**: < 0 (bottom left)
- **IV**: < 0 (bottom right)

Points ON the axes don't belong to any quadrant. (a, 0) sits on the -axis; (0, b) sits on the -axis.

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