Coordinate Plane

Vocabulary Coordinate Coordinate Plane Ordered Pairs Origin Plot Quadrants X-axis Y-axis

x y A coordinate plane is a plane containing a horizontal number line, the x-axis, and a vertical number line, the y axis. The intersection of these axes is called the origin. 5 y-axis 4 Quadrant II 3 Quadrant I 2 x-axis 1 –5 –4 –3 –2 –1 Origin 1 2 3 4 5 –1 –2 Quadrant III –3 Quadrant IV –4 –5 The axes divide the coordinate-plane into four regions called quadrants, which are numbered I, II, III, and IV.

Identify the quadrant that contains each point. Example 1 Identify the quadrant that contains each point. x y –2 2 –4 4 –1 –3 –5 5 3 1 A. Point S W Point S lies in quadrant IV. T B. Point T Point T lies in quadrant I. C. Point W S Point W lies on the y-axis between Quadrants I and II

Point N lies in quadrant II. Practice Identify the quadrant that contains each point. x y –2 2 –4 4 –1 –3 –5 5 3 1 A. Point N Point N lies in quadrant II. N B. Point X Y Point X lies in quadrant III. C. Point Y Point Y lies on the origin. X

Finding Quadrant of a Point By Using Ordered Pairs

Points on a coordinate plane are identified by ordered pairs Points on a coordinate plane are identified by ordered pairs. An ordered pair consists of two numbers in a certain order. The origin is the point (0,0). Ordered pairs are sometimes called coordinates. x y –2 2 –4 4 –1 –3 –5 5 3 1 2 units up 3 units right Ordered pair (3, 2) x-coordinate y-coordinate Units right or left from 0 Units up or down from 0

Plot (this means to graph) each point on a coordinate plane. Example 2 Plot (this means to graph) each point on a coordinate plane. x y –2 2 –4 4 –1 –3 –5 5 3 1 A. Point D (3, 3) D Start at the origin. Move 3 units right and 3 units up. B. Point E (–2, –3) Start at the origin. Move 2 units left and 3 units down. E F C. Point F (3, –5) Start at the origin. Move 3 units right and 5 units down.

Start at the origin. Move 4 units right and 4 units up. Practice Plot each point on a coordinate plane. x y –2 2 –4 4 –1 –3 –5 5 3 1 A. D (4, 4) E D Start at the origin. Move 4 units right and 4 units up. B. E (–2, 3) F Start at the origin. Move 2 units left and 3 units up. C. F (–1, –2) Start at the origin. Move 1 unit left and 2 units down.

Give the coordinates of each point. Example 3 Give the coordinates of each point. x y –2 2 –4 4 –1 –3 –5 5 3 1 A. Point X (–2, 5) X Start at the origin. Point X is 2 units left and 5 units up. Y B. Point Y (–1, 0) Start at the origin. Point Y is one unit left on the x-axis. Z C. Point Z (3, –3) Start at the origin. Point Z is 3 units right and 3 units down.

Start at the origin. Point L is 4 units left and 3 units up. Practice Give the coordinates of each point. x y –2 2 –4 4 –1 –3 –5 5 3 1 A. Point L (–4, 3) N L Start at the origin. Point L is 4 units left and 3 units up. B. Point M (–2, –2) M Start at the origin. Point M is 2 units left and 2 units down. C. Point N (3, 4) Start at the origin. Point N is 3 units right and 4 units up.

Identify the quadrant that contains each description. Example 4 Identify the quadrant that contains each description. x y –2 2 –4 4 –1 –3 –5 5 3 1 A. Positive x-coordinate and a negative y-coordinate Quadrant IV B. Negative x-coordinate and a negative y-coordinate Quadrant III. C. X-coordinate of 0 On the y-axis

Give the coordinates for the following points: star lightning circle heart cross triangle moon square diamond music note

End of Today’s lesson

Reflections of Point on a Coordinate Plane Two points are reflections of each other if the x-axis or y-axis forms a line of symmetry for the two points. This means that if you folded the graph along that axis, the two points would line up.

Reflections of Point on a Coordinate Plane You can find the reflections of points by looking at the signs of each coordinate.

Reflection across the x-axis The coordinate plane shows that point (-3, 2) and (-3, -2) are the same distance from the x-axis in opposite directions. So, they are reflected across the x-axis. When a point is reflected across the x axis, the x-coordinates stays the same and the y-coordinates are opposites.

Reflection across the y-axis The coordinate plane shows that point (-4, 0) and (4, 0) are the same distance from the y-axis in opposite directions. So, they are reflected across the y-axis. When a point is reflected across the y axis, the y-coordinates stays the same and the x-coordinates are opposites.

Determine Reflection using Ordered Pairs What axis are the following points reflected across? (3,-2) and (-3, -2) Because the y-coordinates remained the same, these points are reflected across the y-axis. (5, 2) and (5, -2) Because the x-coordinates remained the same, these points are reflected across the x-axis.

White Board Practice What axis are these points reflected across? (2, 7) and (-2, 7) (5, 3) and (-5, 3) (-1, 4) and (-1, -4) (-7, 1) and (-7, -1) (5, -6) and (5, 6) (-2, 4) and (-2, -4) (8, -3) and (-8, -3)

Reflections of Point on a Coordinate Plane Graph the reflection of the following points. (4, -2) across the x (6, 7) across the y (-5, 3) across the y (-6, -2) across the x (1,6) across the y (9, 10) across the x

End of today’s lesson

Review coordinate plane, plotting points, and reflections

Determine which letter is at each coordinate: (4,9) (-10,9) (-4,-2) (6,-5) (3,5) (6,7) (3, -4) (6, -4) (6, -8) (10,7) Label each quadrant. Which quadrant has (+,+) coordinates? Which quadrant has (+,-) coordinates? Which quadrant has (-,+) coordinates? Which quadrant has (-,-) coordinates?

Graph the following points on your graph paper. (-5, 9) (4,3) (-9, -9) (1,0) (0,4) (2,-1) (10, -10) (-4, 7) (5, 7) (-3, 8)

White Board Practice What axis are these points reflected across? (14, 9) and (-14, 9) (8, 23) and (-8, 23) (-16, 42) and (-16, -42) (-29, 15) and (-29, -15) (12, -16) and (12, 16) (-22, 34) and (-22, -34) (78, -93) and (-78, -93)

What are the coordinates of the reflected points? (-2, 4) reflect across the y-axis (5, -7) reflect across the x-axis (-7, 10) reflect across the x-axis (-5, 24) reflect across the y-axis (92, -45) reflect across the y-axis (62, -52) reflect across the x-axis (-21, 41) reflect across the y-axis (26, 92) reflect across the y-axis (31, -12) reflect across the x-axis (-82, -22) reflect across the y-axis