Coordinate Geometry Chapter 7 Exercise 7.2

What is the distance between the origin O(0, 0) and the point P(5, 0)?

What formula is used to calculate the distance between two points in a coordinate plane?

What is the distance between the origin O(0, 0) and the point Q(6, 8)?

Which of the following is true about the distance OQ?

If the coordinates of point P were (5, 5), what would be the distance OP?

Distance Formula

The distance between two points ( O(x_1, y_1) ) and ( P(x_2, y_2) ) is calculated using the formula:
[ OP = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

Example Calculations

For points ( O(0, 0) ) and ( P(5, 0) ):
- Calculation:
  [ OP = \sqrt{(5 - 0)^2 + (0 - 0)^2} ]
  [ OP = \sqrt{5^2 + 0^2} ]
  - Result: ( OP = 5 )
- This value represents both the radius of a circle centered at the origin and the distance from the origin to point P.
For points ( O(0, 0) ) and ( Q(6, 8) ):
- Calculation:
  [ OQ = \sqrt{(6 - 0)^2 + (8 - 0)^2} ]
  [ OQ = \sqrt{6^2 + 8^2} ]
  [ OQ = \sqrt{36 + 64} ]
  [ OQ = \sqrt{100} ]
  - Result: ( OQ = 10 )
- This distance also demonstrates the application of the distance formula in identifying the radius or direct distance from the origin to point Q.

Key Outcomes

The distances calculated demonstrate the principles of coordinate geometry, providing a foundation for understanding more complex geometric concepts.
Both examples reinforce the understanding of the Pythagorean theorem within the context of the Cartesian plane.

Test your knowledge on calculating distances in coordinate geometry with this quiz. Focused on Chapter 7, Exercise 7.2, you'll solve problems involving distances from the origin and between points. Sharpen your skills in this essential math topic!