The Coordinate Plane Unit 1 Lesson 12 The Coordinate Plane Students will be able to: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. Find and position integers on a coordinate plane Find and position pairs of integers on a coordinate plane. Key Vocabulary: Axis Quadrants Coordinates The Coordinate Plane A coordinate plane is formed by two number lines in a plane that intersect at right angles. ๐ The point of intersection is the zero on each. The two number lines are called the axis. Quadrant II 5 4 Origin 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -3 -4 Quadrant IV -5 Quadrant III Quadrant I ๐ The Coordinate Plane The horizontal axis is called the x-axis. The vertical axis is called the y-axis. ๐ The two axes divide the coordinate plane into four quadrants. The point where the axes intersect is called the origin. Quadrant II 5 4 Origin 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -3 -4 Quadrant IV -5 Quadrant III Quadrant I ๐ The Coordinate Plane Sample Problem 1: Name the quadrant where each point is located. ๐ a. ๐ฉ 5 4 ๐จ 3 2 1 -5 -4 -3 -2 -1 ๐ซ 0 1 2 3 4 5 -2 -3 -4 -5 ๐ช ๐ The Coordinate Plane Sample Problem 1: Name the quadrant where each point is located. ๐ a. ๐จ โ ๐๐ฎ๐๐๐ซ๐๐ง๐ญ ๐ ๐ฉ โ ๐๐ฎ๐๐๐ซ๐๐ง๐ญ ๐๐ ๐ช โ ๐๐ฎ๐๐๐ซ๐๐ง๐ญ ๐๐ ๐ซ โ ๐๐ฎ๐๐๐ซ๐๐ง๐ญ ๐๐๐ ๐ฉ 5 4 ๐จ 3 2 1 -5 -4 -3 -2 -1 ๐ซ 0 1 2 3 4 5 -2 -3 -4 -5 ๐ช ๐ The Coordinate Plane Sample Problem 1: Name the quadrant where each point is located. ๐ b. 5 4 ๐ฒ -5 -4 -3 -2 -1 ๐ด ๐ต 3 2 1 0 1 2 3 4 5 -2 -3 -4 -5 ๐ฑ ๐ The Coordinate Plane Sample Problem 1: Name the quadrant where each point is located. ๐ b. ๐ด โ ๐๐ฎ๐๐๐ซ๐๐ง๐ญ ๐๐๐ ๐ต โ ๐๐ฎ๐๐๐ซ๐๐ง๐ญ ๐ ๐ฒ โ ๐๐ฎ๐๐๐ซ๐๐ง๐ญ ๐๐ ๐ฑ โ ๐๐ฎ๐๐๐ซ๐๐ง๐ญ ๐๐ 5 4 ๐ฒ -5 -4 -3 -2 -1 ๐ด ๐ต 3 2 1 0 1 2 3 4 5 -2 -3 -4 -5 ๐ฑ ๐ The Coordinate Plane An ordered pair gives the location of a point on a coordinate plane. The first number tells how far to move right (positive) or left (negative) from the origin. The second number tells how far to move up (positive) or down (negative). The Coordinate Plane The numbers in an ordered pair are called coordinates. The first number is called the x-coordinate. The second number is called the y-coordinate. The ordered pair for the origin is (0,0). The Coordinate Plane Sample Problem 2: Graph each point on a coordinate plane. a. ๐จ (๐, ๐) ๐ฉ (โ๐, ๐) ๐ช (๐, โ๐) ๐ซ โ๐, โ๐ ๐ฌ ๐, โ๐ ๐ญ โ๐, ๐ The Coordinate Plane Sample Problem 2: Graph each point on a coordinate plane. ๐ a. ๐จ (๐, ๐) 5 ๐จ 4 ๐ฉ ๐ฉ (โ๐, ๐) 3 2 ๐ช (๐, โ๐) 1 ๐ญ ๐ซ โ๐, โ๐ ๐ฌ ๐, โ๐ ๐ญ โ๐, ๐ -5 -4 -3 -2 -1 ๐ฌ ๐ซ 0 1 2 3 4 5 -2 -3 -4 -5 ๐ช ๐ The Coordinate Plane Sample Problem 3: Give the coordinates of each point. ๐ a. 5 4 3 2 1 ๐ฒ ๐ด -5 -4 -3 -2 -1 ๐ท ๐น ๐ณ 0 1 2 3 4 5 -2 -3 -4 -5 ๐ป ๐ The Coordinate Plane Sample Problem 3: Give the coordinates of each point. ๐ a. 5 4 3 2 1 ๐ฒ ๐ด -5 -4 -3 -2 -1 ๐ท ๐น ๐ณ 0 1 2 3 4 5 -2 -3 -4 -5 ๐ป ๐ ๐ฒ (โ๐, ๐) ๐ณ (๐, ๐) ๐ด (โ๐, ๐) ๐ท โ๐, โ๐ ๐น ๐, โ๐ ๐ป ๐, โ๐ The Coordinate Plane Finding Segment Lengths and Area Sample Problem 4: Graph each point on a coordinate plane and find the line segment lengths. a. ๐จ โ๐, ๐ ๐๐๐ ๐ฉ โ๐, ๐ ๐ฎ ๐, ๐ ๐๐๐ ๐ป ๐, โ๐ ๐ช โ๐, โ๐ ๐๐๐ ๐ฒ(โ๐, โ๐) The Coordinate Plane Sample Problem 4: Graph each point on a coordinate plane and find the line segment lengths. ๐ a. ๐ฉ ๐ ๐จ -5 -4 -3 -2 -1 5 4 3 2 1 0 1 2 3 4 5 -2 -3 -4 -5 ๐จ๐ฉ is horizontal ๐จ๐ฉ = ๐ ๐๐๐๐๐๐๐๐๐ ๐๐ ๐ โ ๐๐๐๐๐ ๐๐๐๐๐๐ ๐จ๐ฉ = โ๐ โ (โ๐) = โ๐ + ๐ = ๐ ๐จ๐ฉ = ๐ ๐๐๐๐๐ The Coordinate Plane Sample Problem 4: Graph each point on a coordinate plane and find the line segment lengths. ๐ a. 5 4 3 2 1 ๐ -5 -4 -3 -2 -1 ๐ฎ๐ป is vertical ๐ฎ๐ป = ๐ ๐๐๐๐๐๐๐๐๐ ๐๐ ๐ โ ๐๐๐๐๐ ๐๐๐๐๐๐ ๐ฎ๐ป = ๐ โ (โ๐) = ๐ + ๐ = ๐ ๐ฎ 0 1 2 3 4 5 -2 -3 -4 -5 ๐ป ๐ฎ๐ป = ๐ ๐๐๐๐๐ The Coordinate Plane Sample Problem 4: Graph each point on a coordinate plane and find the line segment lengths. ๐ a. 5 4 3 2 1 ๐ -5 -4 -3 -2 -1 ๐ฒ ๐ช 0 1 2 3 4 5 -2 -3 -4 -5 ๐ฒ๐ช is vertical ๐ฒ๐ช = ๐ ๐๐๐๐๐๐๐๐๐ ๐๐ ๐ โ ๐๐๐๐๐ ๐๐๐๐๐๐ ๐ฒ๐ช = โ๐ โ (โ๐) = โ๐ + ๐ = ๐ ๐ฒ๐ช = ๐ ๐๐๐๐๐ The Coordinate Plane Sample Problem 5: Graph each point on a coordinate plane and find the area of the figure. a. ๐จ ๐, ๐ , ๐ฉ โ๐, ๐ , ๐ช โ๐, โ๐ ๐๐ง๐ ๐ซ ๐, โ๐ The Coordinate Plane Sample Problem 5: Graph each point on a coordinate plane and find the area of the figure. ๐ a. ๐ฉ ๐ -5 -4 -3 -2 -1 ๐ช 5 4 3 2 1 ๐จ ๐จ๐ฉ = ๐ ๐๐๐๐๐๐๐๐๐ ๐๐ ๐ โ ๐๐๐๐๐ ๐๐๐๐๐๐ ๐จ๐ฉ = ๐ โ (โ๐) = ๐ + ๐ = ๐ 0 1 2 3 4 5 -2 -3 -4 -5 ๐จ๐ฉ horizontal ๐ซ ๐จ๐ฉ = ๐ ๐๐๐๐๐ The Coordinate Plane Sample Problem 5: Graph each point on a coordinate plane and find the area of the figure. ๐ a. ๐ฉ ๐ -5 -4 -3 -2 -1 ๐ช 5 4 3 2 1 ๐จ ๐ฉ๐ช = ๐ ๐๐๐๐๐๐๐๐๐ ๐๐ ๐ โ ๐๐๐๐๐ ๐๐๐๐๐๐ ๐ฉ๐ช = ๐ โ (โ๐) = ๐ + ๐ = ๐ 0 1 2 3 4 5 -2 -3 -4 -5 ๐ฉ๐ช is vertical ๐ซ ๐ฉ๐ช = ๐ ๐๐๐๐๐ The Coordinate Plane Sample Problem 5: Graph each point on a coordinate plane and find the area of the figure. ๐ a. ๐ฉ ๐ -5 -4 -3 -2 -1 ๐ช 5 4 3 2 1 ๐จ ๐จ = ๐จ๐ฉ โ ๐ฉ๐ช 0 1 2 3 4 5 -2 -3 -4 -5 Rectangle ๐จ = ๐ ๐๐๐๐๐ โ ๐ ๐๐๐๐๐ ๐จ = ๐๐ ๐๐๐๐๐๐ ๐ซ