Distance And Midpoints
Muhtasari
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.
Malengo
- Calculate the distance between two points using the distance formula
- Find the coordinates of a point dividing a line in a given ratio
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Tathmini ya Somo
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Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- 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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Vitabu Vinavyopendekezwa
Jifunze zaidi kutoka vyanzo huria
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Sehemu ya kitabu
The Rectangular Coordinate Systems and Graphs
Plot ordered pairs in a Cartesian coordinate system.
"College Algebra: The Rectangular Coordinate Systems and Graphs" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/2-1-the-rectangular-coordinate-systems-and-graphs. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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