{"id":694,"date":"2025-10-15T10:21:51","date_gmt":"2025-10-15T10:21:51","guid":{"rendered":"https:\/\/kapdec.com\/help\/?post_type=docs&p=694"},"modified":"2026-04-13T06:29:12","modified_gmt":"2026-04-13T06:29:12","slug":"what-are-the-basic-elements-of-geometry","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/what-are-the-basic-elements-of-geometry\/","title":{"rendered":"What Are the Basic Elements of Geometry?"},"content":{"rendered":"

Geometry Basic Elements:\u00a0<\/b><\/p>\n

 <\/p>\n

A lot of the geometric shapes and figures you have learned thus far will eventually have formulas assigned to them as you delve into the world of algebra and more advanced geometry. In order for those formulas to make physical, geometric sense, they need to be placed in what is called a coordinate plane. In this lesson, we will learn the properties of the coordinate plane and how to graph points on it.<\/p>\n

 <\/p>\n

 <\/p>\n

Properties of the Coordinate Plane<\/b><\/p>\n

To the right\u00a0is the Cartesian coordinate plane. Because we are not going to be using any other coordinate plane in the near future, and it is the standard coordinate plane for math students all around the world, we will call it simply the Coordinate Plane.\u00a0X<\/i><\/p>\n

 <\/p>\n

The thick black lines are called the \u201caxes\u201d (plural of the word axis). The horizontal \u2013 right-to-left \u2013 axis is called the \u201cx axis\u201d, as indicated by the x to the left of the coordinate plane. The vertical \u2013 up-to-down \u2013 axis is called the \u201cy axis\u201d, as indicated by the y directly above the coordinate plane. The arrows indicate that the axes go on to infinity.<\/p>\n

 <\/p>\n

The numbers along each axis are values a point can have: x-values and y-values. As you go farther to the right, the x-values increase in the positive direction, and as you go farther to the left, the x-values decrease in the negative direction. Similarly, as you go up, the y-values increase in the positive direction, and as you go down, the y-values decrease in the negative direction.<\/p>\n

 <\/p>\n

There are four quadrants to the Coordinate Plane: I, II, III, and IV, the Roman numerals for 1, 2, 3, and 4. They are color-coded and labeled on the Coordinate Plane above.<\/p>\n

 <\/p>\n

Lastly, any point on the Coordinate Plane is defined by what is called an \u201cordered pair\u201d enclosed in parentheses like this: (x,y). The x-value always comes first. For example, the orange point in Quadrant II has an ordered pair of (-3,4).<\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

Example<\/b>:<\/p>\n

Plot the points defined by the following ordered pairs:<\/p>\n

(2, 3)<\/p>\n

(-4, -4)<\/p>\n

(-1, -3)<\/p>\n

(4, 0)<\/p>\n

Solution:<\/b><\/p>\n

What Are the Basic Elements of Geometry?<\/h1>\n

Geometry Basic Elements:\u00a0<\/b><\/p>\n

 <\/p>\n

A lot of the geometric shapes and figures you have learned thus far will eventually have formulas assigned to them as you delve into the world of algebra and more advanced geometry. In order for those formulas to make physical, geometric sense, they need to be placed in what is called a coordinate plane. In this lesson, we will learn the properties of the coordinate plane and how to graph points on it.<\/p>\n

 <\/p>\n

 <\/p>\n

Properties of the Coordinate Plane<\/b><\/p>\n

To the right\u00a0is the Cartesian coordinate plane. Because we are not going to be using any other coordinate plane in the near future, and it is the standard coordinate plane for math students all around the world, we will call it simply the Coordinate Plane.\u00a0X<\/i><\/p>\n

 <\/p>\n

The thick black lines are called the \u201caxes\u201d (plural of the word axis). The horizontal \u2013 right-to-left \u2013 axis is called the \u201cx axis\u201d, as indicated by the x to the left of the coordinate plane. The vertical \u2013 up-to-down \u2013 axis is called the \u201cy axis\u201d, as indicated by the y directly above the coordinate plane. The arrows indicate that the axes go on to infinity.<\/p>\n

\"\"<\/p>\n

The numbers along each axis are values a point can have: x-values and y-values. As you go farther to the right, the x-values increase in the positive direction, and as you go farther to the left, the x-values decrease in the negative direction. Similarly, as you go up, the y-values increase in the positive direction, and as you go down, the y-values decrease in the negative direction.<\/p>\n

 <\/p>\n

There are four quadrants to the Coordinate Plane: I, II, III, and IV, the Roman numerals for 1, 2, 3, and 4. They are color-coded and labeled on the Coordinate Plane above.<\/p>\n

 <\/p>\n

Lastly, any point on the Coordinate Plane is defined by what is called an \u201cordered pair\u201d enclosed in parentheses like this: (x,y). The x-value always comes first. For example, the orange point in Quadrant II has an ordered pair of (-3,4).<\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

Example<\/b>:<\/p>\n

Plot the points defined by the following ordered pairs:<\/p>\n

(2, 3)<\/p>\n

(-4, -4)<\/p>\n

(-1, -3)<\/p>\n

(4, 0)<\/p>\n

Solution:<\/b><\/p>\n

\"\"<\/p>\n

 <\/p>\n

Line<\/b><\/p>\n

\"\"<\/p>\n

 <\/p>\n

Ray<\/b><\/p>\n

\"\"<\/p>\n

Key Points<\/b><\/p>\n

    \n
  • The Cartesian Coordinate Plane is a 2-dimensional plane in which points, shapes, and functions can be easily displayed.<\/li>\n
  • Every point on the Coordinate Plane is assigned an ordered pair (x,y), with x indicating its horizontal position and y indicating its vertical position.<\/li>\n
  • Real-world situations can be mapped onto the coordinate plane for ease of problem solving.<\/li>\n<\/ul>\n

    Did You Know?<\/b><\/p>\n

      \n
    • The Cartesian Coordinate Plane was developed by French mathematician (and philosopher) Rene Descartes in 1637.<\/li>\n
    • Descartes\u2019s ideas, including the Coordinate Plane, were very helpful for the development of Newton\u2019s ideas and mathematics.<\/li>\n
    • Descartes is also considered by many to be the father of Western philosophy.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

      Geometry Basic Elements:\u00a0   A lot of the geometric shapes and figures you have learned thus far will eventually have formulas assigned to them as you delve into the world of algebra and more advanced geometry. In order for those formulas to make physical, geometric sense, they need to be placed in what is called […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[591],"tags":[596],"class_list":["post-694","post","type-post","status-publish","format-standard","hentry","category-grade-6","tag-grade-6-mathematics"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/694","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=694"}],"version-history":[{"count":1,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/694\/revisions"}],"predecessor-version":[{"id":1570,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/694\/revisions\/1570"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=694"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=694"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}