Distance And Midpoints
Bayani Gaba-gaba
Every coordinate geometry problem starts with the same raw material: a pair of points on the Cartesian plane. From those two points you can measure exactly how far apart they are, find the point that sits exactly halfway between them, or locate the point that divides the segment in any ratio you choose. These three skills unlock the rest of coordinate geometry, from proving that a shape is a particular quadrilateral to finding the centre of a circle.
In this topic you will master the distance formula, the midpoint formula, and the section formula for dividing a line segment in a given ratio. Each formula has a clean derivation from ideas you already know, and the worked examples build from straightforward substitution to multi-step problems where you combine all three tools together.
Manufura
- Calculate the distance between two points using the distance formula
- Find the coordinates of a point dividing a line in a given ratio
Takardar Darasi
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Nazarin Darasi
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- What is the distance between the points (1, 2) and (4, 6)? A) 4 B) 5 C) 7 D) 25 Answer: B
- The midpoint of (3, -1) and (7, 5) is: A) (4, 4) B) (5, 2) C) (10, 4) D) (2, 3) Answer: B
- A point divides the segment from (0, 0) to (8, 12) in the ratio 1 : 3. What are its coordinates? A) (2, 3) B) (4, 6) C) (6, 9) D) (3, 4) Answer: A
- The distance between (-2, 3) and (4, -5) is: A) 8 B) 10 C) 14 D) 100 Answer: B
- If the midpoint of A(x, 4) and B(6, 10) is (5, 7), what is x? A) 2 B) 4 C) 5 D) 11 Answer: B
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Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.
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Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.
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