One-to-one Correspondence Two sets have a one-to-one correspondence if every element in one set is paired with one and only one element in the other set and no elements in either remain unpaired.

Cartesian coordinate plane Rectangular coordinate plane

“y” 6 “x” origin −6 6 −6

x-axis — the horizontal number line in a plane y-axis — the vertical number line in a plane origin — the point at which the x-axis and y-axis intersect

Ordered Pair An ordered pair is a pair of numbers written in parentheses used to locate a particular point in the coordinate plane.

A (4, −3) x-coordinate y-coordinate

y 6 x −6 6 A −6 A (4, −3)

Origin (0, 0) x-axis (x, 0) y-axis (0, y)

Example 1 Give the coordinates and quadrant location of each point: P, Q, R, S.

y Q (3, 2) P (−2, 4) x R (5, 0) S (2, −5)

Example 2 Graph each point. J (2, 4) K (−1, −2) L (−3, 3) M (0, −5)

y L J (2, 4) (−3, 3) x K (−1, −2) M (0, −5) J (2, 4) K (−1, −2)

Example Graph each point. (0, 0), (−2, 3), (4, 5), (4, 0), (3, −1), (−2, −1), (0, −3)

y (0, 0) (−2, 3) (4, 5) (4, 0) (−2, 3) (4, 5) x (0, 0) (4, 0)

y (3, −1) (−2, −1) (0, −3) x (3, −1) (−2, −1) (0, −3)

Example Which of the points from the previous question is at the origin? On the x-axis only? On the y-axis only? In the first quadrant? (0, 0) (4, 0) (0, −3) (4, 5)

Example In the second quadrant? (−2, 3) In the fourth quadrant? (3, −1)

Example How can we identify easily whether a point is on the x-axis? The y-coordinate is 0.

Example How can we identify easily whether a point is on the y-axis? The x-coordinate is 0.

Example How can we identify which quadrant a point is in? based on the signs of the coordinates

Example Name two points on the x-axis a distance of 5 from the origin. (5, 0), (−5, 0)

Example Name two points on the y-axis a distance of 3 from the origin. (0, 3), (0, −3)

Exercise Using the coordinate plane, name the point located by each ordered pair.

(2.5, 5) y B B E I C J D x F K G L H A

(2, −1.5) y B E I C J D x F F K G L H A

(0, 3) y B E I C C J D x F K G L H A

(−3, 4.5) y B E E I C J D x F K G L H A

(4, −5) y B E I C J D x F K G L H A A

(−3, −4.5) y B E I C J D x F K G L H H A

(−2, −3) y B E I C J D x F K G G L H A

(4, 4) y B E I I C J D x F K G L H A

(−3.5, 2.5) y B E I C J J D x F K G L H A

(−2.5, 0) y B E I C J D D x F K G L H A

(5, −2.5) y B E I C J D x F K K G L H A

(0, −4) y B E I C J D x F K G L L H A