The gap between (0, 0) and (6, 8) is 10 and the gap between (2, 3) and (5, 7) is 5, so this Class 10 sheet turns the distance formula into repeated practice. The key also gives a midpoint of (4, 5) and a distance of 13 for a later pair.
Key Takeaways
The distance between (0, 0) and (6, 8) is 10 (Q1).
The distance between (2, 3) and (5, 7) is 5 (Q2).
The key records midpoint (4, 5) and distance 13.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The distance between the points (0, 0) and (6, 8) is
(a) 6(b) 8(c) 10(d) 14
2.The distance between the points (2, 3) and (5, 7) is
(a) 4(b) 5(c) 7(d) 9
3.The midpoint of the line segment joining (1, 1) and (7, 9) is
(a) (3, 4)(b) (4, 5)(c) (5, 6)(d) (8, 10)
4.The distance between the points (0, 0) and (5, 12) is
(a) 13(b) 7(c) 17(d) 60
5.The midpoint of the line segment joining (4, 8) and (6, 12) is
(a) (5, 10)(b) (2, 4)(c) (10, 20)(d) (4, 10)
6.The distance between the points (-1, 1) and (3, 4) is
(a) 3(b) 4(c) 5(d) 6
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the distance formula between the points (x₁, y₁) and (x₂, y₂).
8.Find the distance between the points (0, 0) and (8, 6).
9.Write the midpoint formula for the points (x₁, y₁) and (x₂, y₂).
10.Find the midpoint of the points (3, 5) and (7, 9).
11.Find the distance between the points (2, 2) and (6, 5).
12.Find the midpoint of the line segment joining (0, 0) and (4, 4).
13.A point lies on the x-axis at a distance of 6 units from the origin. Write its coordinates.
14.Find the distance between the points (4, 0) and (0, 3).
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Show that the points (0, 0), (3, 0) and (0, 4) form a right triangle, and find its area.
16.Find the midpoint of the line segment joining (4, 5) and (8, 9).
17.Find the point on the x-axis which is equidistant from (2, 3) and (4, 1).
18.Find the distance between the points (a, 0) and (0, b).
19.A point P divides the line segment joining (2, 3) and (4, 7) in the ratio 1 : 1. Find the coordinates of P.
20.Show that the points (1, 1), (4, 4) and (1, 4) form a right isosceles triangle.
Answer Key
1. c) 10
2. b) 5
3. b) (4, 5)
4. a) 13
5. a) (5, 10)
6. c) 5
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the distance between (0, 0) and (6, 8)?
10, option (c) in this worksheet (Q1).
What is the distance between (2, 3) and (5, 7)?
5, option (b) in this worksheet (Q2).
What is the midpoint of (2, 3) and (6, 7)?
(4, 5), from the answer key on this page.
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