Class 10 Maths Chapter 7 Coordinate Geometry – Exercise 7.1 NCERT Solutions

Introduction

Exercise 7.1 introduces the distance formula in coordinate geometry. It helps calculate the distance between two points in the Cartesian plane. This exercise builds the foundation for solving problems involving points, lines, and geometric figures using coordinates.

Formula Used

Distance Formula: For two points $P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2})$ ,

PQ=(x2−x1)2+(y2−y1)2

NCERT Questions with Solutions (10)

Q1. Find distance between points (2, 3) and (4, 1).

Solution: $P Q = \sqrt{(4 - 2)^{2} + (1 - 3)^{2}} = \sqrt{4 + 4} = \sqrt{8} = 2 \sqrt{2}$ .

Q2. Find distance between points (-5, 7) and (-1, 3).

Solution: $P Q = \sqrt{(- 1 + 5)^{2} + (3 - 7)^{2}} = \sqrt{16 + 16} = \sqrt{32} = 4 \sqrt{2}$ .

Q3. Find distance between points (0, 0) and (6, 8).

Solution: $P Q = \sqrt{(6 - 0)^{2} + (8 - 0)^{2}} = \sqrt{36 + 64} = \sqrt{100} = 10$ .

Q4. Find distance between points (3, -2) and (-3, -2).

Solution: $P Q = \sqrt{(- 3 - 3)^{2} + (- 2 + 2)^{2}} = \sqrt{36 + 0} = 6$ .

Q5. Find distance between points (7, 4) and (2, 4).

Solution: $P Q = \sqrt{(2 - 7)^{2} + (4 - 4)^{2}} = \sqrt{25} = 5$ .

Q6. Find distance between points (1, 1) and (2, 2).

Solution: $P Q = \sqrt{(2 - 1)^{2} + (2 - 1)^{2}} = \sqrt{1 + 1} = \sqrt{2}$ .

Q7. Find distance between points (-2, -3) and (3, -3).

Solution: $P Q = \sqrt{(3 + 2)^{2} + (- 3 + 3)^{2}} = \sqrt{25 + 0} = 5$ .

Q8. Find distance between points (4, 5) and (1, 1).

Solution: $P Q = \sqrt{(1 - 4)^{2} + (1 - 5)^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$ .

Q9. Find distance between points (-1, -2) and (2, 2).

Solution: $P Q = \sqrt{(2 + 1)^{2} + (2 + 2)^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$ .

Q10. Find distance between points (0, 7) and (0, -7).

Solution: $P Q = \sqrt{(0 - 0)^{2} + (- 7 - 7)^{2}} = \sqrt{0 + 196} = 14$ .

FAQs (10 from NCERT)

Q: What is the distance formula? A: $P Q = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$ .
Q: What is Cartesian plane? A: A plane defined by x‑axis and y‑axis.
Q: What are coordinates? A: Ordered pairs $(x, y)$ representing points.
Q: What is origin? A: Point (0, 0).
Q: What is x‑axis? A: Horizontal axis in Cartesian plane.
Q: What is y‑axis? A: Vertical axis in Cartesian plane.
Q: What is quadrant? A: One of four regions divided by axes.
Q: Can distance be negative? A: No, distance is always non‑negative.
Q: What is distance between a point and itself? A: Zero.
Q: Why is this exercise important? A: It builds foundation for coordinate geometry problems.

Conclusion

Exercise 7.1 has 10 solved questions and 10 FAQs that strengthen your understanding of the distance formula in coordinate geometry. This builds the foundation for advanced topics like section formula and equations of lines in Class 10 Maths.

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