HPTER 9 The oordinate Plane 9. 9. 9. Points on the oordinate Plane Length of Line Segments Real-World Problems: Graphing Have ou ever used a street director? street director is useful for locating a street in an unfamiliar area. The maps in the director use a sstem of coordinates to help ou locate the streets easil. When using a director, ou can look for a street name in the inde. The inde gives ou the correct map to look at and also gives a pair of coordinates so that ou can locate the street. For eample, in the map below, Fort Hill Road can be found on map 87, section. is a pair of coordinates that tells ou the location of the street on the map. In this chapter, ou will use numerical coordinates to locate points on a coordinate plane. 5 Nature entre IG IE St.ndrew Golf lub Sprain rook Pkw Sprain Lake Golf ourse Fort Hill Rd entral Park ve Greenville 00 eech Hill Old rm Rd rook Rd Popham Rd Post Rd Harwood Park utler Field Heathcole Rd rake Rd Ever point on the coordinate plane can be represented b a pair of coordinates. Map 87 8 hapter 9 The oordinate Plane
Recall Prior Knowledge Identifing and plotting coordinates O 5 The coordinates of O, the origin, are (0, 0). To find the location of point, move units to the right on the -ais and unit up on the -ais. The coordinates of are (, ). Quick heck Use the coordinate plane below. 5 0 5 6 Give the coordinates of points,, and. Use graph paper. Plot the points on a coordinate plane. P (, ), Q (, ), and R (0, ). hapter 9 The oordinate Plane 9
Representing negative numbers on the number line Negative numbers are numbers less than zero., 0,, and are eamples of negative numbers. Negative numbers are found to the left of 0 on the number line. 7 6 5 0 5 6 Quick heck Identif the number that each indicated point represents.???? 0 5 0 raw a horizontal number line to represent each set of numbers., 0,, 5, 8 5 5,, 9, 7, Recognizing and writing the absolute value of a number The absolute value of a number is the distance from itself to 0 on the number line. It is alwas positive. 5 0 5 units units is units awa from 0. Its absolute value is. Similarl, the absolute value of is also. You can write 5, and 5. Quick heck Use the smbol to write the absolute values of the following numbers. 6 7 6 8 0 hapter 9 The oordinate Plane
Finding the perimeter of a polgon The perimeter of a polgon is the distance around it. Figure E has 5 sides,,, E, and E. The perimeter of figure E is equal to the sum of the lengths of its 5 sides: 9 cm 9 cm E E E 7 cm 7 cm 5 9 7 7 7 9 5 9 cm 7 cm Quick heck Find the perimeter of each polgon. 7 Figure is an isosceles triangle. 8 Figure EF is an equilateral triangle. 8 in. in. E F 5 in. 9 Figure PQRS is a trapezoid. 0 Figure WXYZ is a parallelogram. P 6 cm S W Z 9 cm 9 cm 8 cm Q 0 cm R X 7 cm Y Figure JKLM is a rhombus. 6 m J K M L hapter 9 The oordinate Plane
9. Points on the oordinate Plane Lesson Objectives Name and locate points on the coordinate plane. raw and identif polgons on the coordinate plane. Vocabular coordinates -ais quadrants coordinate plane -ais Learn Find the coordinates of points on a coordinate plane. The coordinate plane is made up of two number lines that intersect at right angles. The horizontal line is called the -ais and the vertical line is called the -ais. The point of intersection, usuall labeled O, is the origin. The -ais and -ais divide the coordinate plane into four parts called quadrants. Moving counterclockwise around the origin, the quadrants are named Quadrant I, Quadrant II, Quadrant III, and Quadrant IV. Quadrant II 6 5 F Quadrant I G 6 5 O E 5 6 Quadrant III 5 6 H Quadrant IV hapter 9 The oordinate Plane
Point is in the first quadrant. Point is units to the right of the origin, so its -coordinate is. It is units up from the origin, so its -coordinate is. The coordinates of are (, ). (, ) is called an ordered pair. You can write (, ) to represent the location of. aution The -coordinate comes first in an ordered pair. The ordered pair (, ) does not name the same point as (, ). Point is in the second quadrant. Point is units to the left of the origin, so its -coordinate is. It is units up from the origin, so its -coordinate is. The coordinates of are (, ). Points and are smmetrical about the -ais. Point is said to be the reflection of point across the -ais. You can also sa point is the reflection of point across the -ais. Point is in the third quadrant. Point is units to the left of the origin, so its -coordinate is. It is units down from the origin, so its -coordinate is. The coordinates of are (, ). Points and are reflections of each other across the -ais. Point is in the fourth quadrant. Point is units to the right of the origin, so its -coordinate is. It is units down from the origin, so its -coordinate is. The coordinates of are (, ). Points and are reflections of each other across the -ais. Points E lies on the -ais. It lies between Quadrant I and Quadrant IV. Similarl, point F lies on the -ais. It lies between Quadrant I and Quadrant II. Point G lies on the -ais. It is between Quadrant II and Quadrant III. Point H lies on the -ais. It is between Quadrant III and Quadrant IV. Lesson 9. Points on the oordinate Plane
Guided Practice Use the coordinate plane below. Give the coordinates of points P, Q, R, S, T, U, and V. In which quadrant is each point located? Q R 7 6 5 0 P 5 6 V S 5 6 U T 7 8 Use graph paper. Plot points (, ), (, ), (5, 0), (0, 5), E (, ), and F (, ) on a coordinate plane. Points P and Q are reflections of each other about the -ais. Give the coordinates of point Q if the coordinates of point P are the following: a) (6, ) b) (, ) c) (, 5) d) (7, ) Points R and S are reflections of each other about the -ais. Give the coordinates of point S if the coordinates of point R are the following: a) (6, ) b) (, ) c ) (, 5) d) (7, ) hapter 9 The oordinate Plane
Learn raw and identif polgons on a coordinate plane. 7 6 W 5 X 7 Z 6 5 0 Q 5 6 P Y R 5 6 7 S You can join points on a coordinate plane to form geometric figures. Points (, 6), (, ), (, ), and (5, 6) are joined to form a parallelogram. The opposite sides of a parallelogram are parallel. Points P (, ), Q (, ), R (, 6), and S (, 5) are joined to form a trapezoid. Points W (5, ), X (7, 0), Y (5, ), and Z (, 0) are joined to form a rhombus. Lesson 9. Points on the oordinate Plane 5
Guided Practice Use graph paper. For each eercise, plot the given points on a coordinate plane. Then join the points in order with line segments to form a closed figure. Name each figure formed. 5 (, ), (6, ), and (, ) 5? (?,? ) 7 6 5 0 5? (?,? ) 5? (?,? ) 6 (, ), E (0, 0), and F (, ) 7 J (, 0), K (0, 5), and L (, 0) 8 P (, ), Q (, ), R (, ), and S (, ) 9 W (, ), X (, ), Y (, 0), and Z (, ) 0 (5, ), (5, ), (, ), and (, ) E (, ), F (5, 5), G (, 5), and H (, ) J (, ), K (, ), L (0, ), and M (, ) P (, 0), Q (0, ), R (, 0), and S (0, ) W (, 0), X (, ), Y (, ), and Z (, ) 6 hapter 9 The oordinate Plane
Materials: IENTIFYING QURILTERLS RWN ON OORINTE PLNE graph paper Work in pairs. STEP Plot four points on a coordinate plane and connect them to form a special quadrilateral such as a parallelogram, a rectangle, or a rhombus. o not let our partner see our quadrilateral. STEP Tell our partner the coordinates of three out of the four coordinates of the points ou plotted in STEP. lso tell our partner the tpe of quadrilateral ou plotted, and in which quadrant the fourth point is located. Have our partner guess the coordinates of the fourth point. Eample 6 5 (, 5) (, ) (?,? ) 6 5 0 5 6 Points (, 5), (, ), (, ), and can be joined to form a rhombus. If point is in Quadrant I, what are the coordinates of point? (, ) STEP Switch roles with our partner and repeat the activit with other quadrilaterals. Lesson 9. Points on the oordinate Plane 7
Practice 9. Use the coordinate plane below. Give the coordinates of each point. In which quadrant is each point located? 0 H 9 8 7 6 5 7 G 6 5 0 E 5 6 7 F 5 6 7 8 9 0 Use graph paper. Plot the points on a coordinate plane. In which quadrant is each point located? (, 7), (, 0), (8, ), (0, 6), E (, 5), and F (6, 7) 8 hapter 9 The oordinate Plane
Use graph paper. Points and are reflections of each other about the -ais. Give the coordinates of point if the coordinates of point are the following: (, ) (, ) 5 (, ) 6 (, ) Use graph paper. Points and are reflections of each other about the -ais. Give the coordinates of point if the coordinates of point are the following: 7 (, ) 8 (, ) 9 (, ) 0 (, ) Use graph paper. For each eercise, plot the given points on a coordinate plane. Then join the points in order with line segments to form a closed figure. Name each figure formed. H (5, ), J (, ), K (, ), and L (, ) R (, ), S (, ), T (, ), and U (7, ) W (5, ), X (6, 5), Y (, 5), and Z (, ) Use graph paper. Plot the points on a coordinate plane and answer each question. a) Plot points (6, 5), (5, ), and (5, 5) on a coordinate plane. b) Figure is a rectangle. Plot point and give its coordinates. c) Figure E is a parallelogram. Plot point E above and give its coordinates. 5 a) Plot points (, ) and (, ) on a coordinate plane. b) Join points and with a line segment. c) is a side of square. Name two possible sets of coordinates that could be the coordinates of points and. 6 Plot points (, 5) and (, ) on a coordinate plane. Figure is a right isosceles triangle. If point is in Quadrant III, give the coordinates of point. 7 Plot points (0, ), (, 0), and (0, ) on a coordinate plane. a) What kind of triangle is triangle? b) Figure is a square. Plot point on the coordinate plane and give its coordinates. Lesson 9. Points on the oordinate Plane 9