Drawing Polygons in the Coordinate Plane

Transcription

1 Lesson 7 Drawing Polgons in the Coordinate Plane 6.G. Getting the idea The following points represent the vertices of a polgon. A(, 0), B(0, ), C(, ), D(, ), and E(0, ) To draw the polgon, plot the points on a coordinate plane. Connect the points in order and then connect point E to point A to form the polgon. D 0 C E A B Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC The polgon has sides, so it is a pentagon. Using the names of the vertices in order, we can name it pentagon ABCDE. The coordinates of the vertices can be used to describe other properties of the figure. Side CD is a vertical line since point C and point D have the same -coordinate. Side DE is a horizontal line since point D and point E have the same -coordinate. Side CB is a horizontal line since point C and point B have the same -coordinate. Sides DE and CB both have a length of units, so the sides are the same length. Lesson 7: Drawing Polgons in the Coordinate Plane 6

2 Eample Quadrilateral QRST is shown on the coordinate plane. Find the length of side RS. 0 T Q R S Strateg Use coordinates of two vertices to find the length of a side. Step Find the coordinates of the vertices. The length of RS is the distance between point R and point S. The coordinates of point R are (, ). The coordinates of point S are (, ). Step Use coordinates to find the length of the side. Solution Since side RS is vertical, the -coordinates of the points are the same. The -coordinates are and. The distance between the two points is the vertical distance between the -coordinates. Use absolute value to find the distance between two points on a coordinate plane. The number is, or units from 0. The number is, or units from 0. Since both points are in the same quadrant, subtract to find the distance. units The distance between point R and point S is units. The length of side RS is units. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC 6 Domain : Geometr

3 Eample Kirsten is planting a flower garden in the shape of a right triangle in one corner of her backard. She draws a triangle on a coordinate plane with vertices D(, ), E(, ), and F(, ). Each unit on the coordinate plane represents foot. Verif that her drawing shows a right triangle. Then find the base and height of the flower garden. Strateg Plot the vertices on a coordinate plane. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Step Plot the vertices on the coordinate plane. Classif the figure. Plot the locations of the vertices D(, ), E(, ), and F(, ). Then connect the points. The figure is a triangle. Side EF is the horizontal base and side DE is the vertical height. Angle E is a right angle, so the figure is a right triangle. Step Find the length of the base, EF. To find the horizontal distance between point E and point F, use the -coordinates. The -coordinate of point E is. The -coordinate of point F is. Since the points are in different quadrants, add to find the distance. units Each unit on the grid represents foot, so the length represents feet. Step Find the height, DE. To find the vertical distance between point D and point E, use the -coordinates. The -coordinate of point D is. The -coordinate of point E is. Since the points are in different quadrants, add to find the distance. units Each unit on the grid represents foot, so the length represents feet. Solution 0 D The drawing shows a right triangle. Both the base and height are feet. E F Lesson 7: Drawing Polgons in the Coordinate Plane 6

4 Eample Trapezoid JKLM is shown on the coordinate plane. Find the lengths of the horizontal sides. J M K L 0 Strateg Use the coordinates of the vertices to find side lengths. Step Find the length of JK. The coordinates of point J are (, ). The coordinates of point K are (, ). To find the horizontal distance, use the -coordinates. The -coordinate of point J is. The -coordinate of point K is. Since the points are in different quadrants, add to find the distance. units Step Find the length of ML. The coordinates of point M are (, ). The coordinates of point L are (, ). To find the horizontal distance, use the -coordinates. The -coordinate of point M is. The -coordinate of point L is. Since the points are in different quadrants, add to find the distance. 8 units Solution The length of JK is units. The length of ML is 8 units. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC 6 Domain : Geometr

5 COACHED EXAMPLE Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Jackson is drawing a map of his classroom. The classroom is in the shape of a rectangle. He draws three vertices at A(, ), B(, ), and C(, ). Determine the coordinates where Jackson should plot point D. Plot the given vertices. Connect the points to draw two sides of the rectangle. Use properties of a rectangle to find the location of point D. A rectangle has opposite sides that are parallel and have the same. In the rectangle, side CD will have the same length as side. Find the length of side AB. To find the horizontal distance, use the -coordinates. The -coordinate of point A is. The -coordinate of point B is. Since the points are in different quadrants, units to find the distance. The length of AB is units. So, the length of must also be units. Find the coordinates of point D. To graph point D, start at point C and move The coordinates of point D are (, ). units to the left. Point D has the same -coordinate as point and the same -coordinate as point. Check the answer. In the rectangle, side AD will have the same length as side. To find the vertical distance, use the -coordinates. The -coordinate of point B is. The -coordinate of point C is. Since the points are in different quadrants, The length of BC is The length of AD is units units. units. The coordinates of point D are. to find the distance. 0 Lesson 7: Drawing Polgons in the Coordinate Plane 6

6 LESSON PRACTICE Use the figure to answer the following questions. 0 H G A B C D F E Classif the polgon. Which sides are vertical? Which sides are horizontal? Name sides that have a length of units. Rectangle WXYZ is shown on the coordinate plane. Each vertical side has a length of Each horizontal side has a length of units units 7 units. units units 7 units A polgon has vertices at (, ), (, ), (, ), and (, ). Which statements describe the polgon? Circle all that appl. A. The figure is a quadrilateral. D. Two pairs of opposite sides are parallel. B. Opposite sides have the same length. E. Two sides are vertical. C. One pair of opposite sides is parallel. F. Two sides are horizontal.. W X Z Y 0 Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC 66 Domain : Geometr

7 A square has vertices (0, ), (0, ), and (, ). What are the coordinates of the missing verte? Use numbers from the bo to complete the missing coordinates. -coordinate: -coordinate: 0 Plot the following points on the coordinate plane. Connect the points in order and then connect point D to point A to form a polgon. A(, ), B(, ), C(, ), D(, ) 0 Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC Classif the figure. Use properties of polgons to justif our answer. Lesson 7: Drawing Polgons in the Coordinate Plane 67

8 6 Line segment FG is a side of right triangle FGH. The length of GH is units and angle G is a right angle. F G 0 Part A What are all of the possible coordinates for point H? Part B What is the area of triangle FGH? 7 A verte of a polgon is located at A(, ). The length of side AB is units. Determine whether each ordered pair could be the coordinates for point B. Select Yes or No. A. (, ) Yes No C. (, ) Yes No B. (, ) Yes No D. (, ) Yes No Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC 68 Domain : Geometr

9 8 Tia drew a rectangle with the following characteristics. Two of the vertices have coordinates (, ) and (, ). The area is square units. The vertices of the figure are all in different quadrants. Find the missing coordinates. Use words, numbers, or models to justif our answer. 9 Two vertices of a parallelogram are located at (, ) and (, ). All vertices of the parallelogram are located in the same quadrant, and the parallelogram has two vertical sides that have a length of units. Complete the parallelogram. Label the coordinates of the vertices. Duplicating an part of this book is prohibited b law. 0 Triumph Learning, LLC (, ) (, ) Carmen wants to put a fence around a square garden. The coordinates of the vertices are (, ), (, ), (, ), and (, ). Each grid square has a side length of feet. How man feet of fencing will Carmen need? Eplain how ou solved the problem. 0 Lesson 7: Drawing Polgons in the Coordinate Plane 69