Distance And Midpoints
Gbogbo ọrọ náà
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.
Ebumnobi
- 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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Ekele diri gi maka imecha ihe karịrị na Distance And Midpoints. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- 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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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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