Parallel And Perpendicular Lines
Gbogbo ọrọ náà
Two lines on a grid can run side by side forever, or cross at a perfect right angle. Both relationships are captured entirely by gradient, the single number that measures a line's steepness. Once you know how gradients behave for parallel and perpendicular lines, a whole family of coordinate-geometry questions opens up.
In this lesson you will learn that parallel lines share the same gradient, while perpendicular lines have gradients whose product is \(-1\), the negative reciprocal rule. You will use these facts to find the equations of lines through given points, the foundation for perpendicular bisectors, tangents and much else.
Ebumnobi
- Know and use the condition for two lines to be parallel or perpendicular.
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Ekele diri gi maka imecha ihe karịrị na Parallel And Perpendicular Lines. 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.
- Two lines are parallel when their gradients are: A. Equal B. Negative reciprocals C. Reciprocals D. Opposite in sign Answer: A
- Two lines are perpendicular when the product of their gradients is: A. 0 B. 1 C. -1 D. Equal Answer: C
- What is the gradient of a line perpendicular to one with gradient 2? A. 2 B. -2 C. 1/2 D. -1/2 Answer: D
- A line is parallel to y = 3x + 2 and passes through (1, 5). Its equation is: A. y = 3x + 2 B. y = -3x + 8 C. y = (1/3)x + 5 D. y = 3x - 5 Answer: A
- The gradient perpendicular to a line of gradient 2/3 is: A. 2/3 B. 3/2 C. -3/2 D. -2/3 Answer: C
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Graphs of Linear Functions
Graph linear functions.
"Precalculus: Graphs of Linear Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/precalculus/pages/2-2-graphs-of-linear-functions. Access for free at https://openstax.org/books/precalculus/pages/1-introduction
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