174 Easy Algebra Step-by-Step
Problem State whether the two ordered pairs are equal. Explain your
answer.
a. (2, 7), (7, 2)
b. (−3, 5), (3, 5)
c. (−4, −1), (4, 1)d. 610
5()^62 ,^2 ,⎛ ,
⎝⎜⎛⎛
⎝⎝⎞
⎠⎟⎞⎞
⎠⎠Solution
a. (2, 7), (7, 2)
Step 1. Check whether the corresponding coordinates are equal.
(2, 7) ≠ (7, 2) because 2 and 7 are not equal.b. (−3, 5), (3, 5)
Step 1. Check whether the corresponding coordinates are equal.
(− 3 , 5) ≠ (3, 5) because −3 ≠ 3.c. (−4, −1), (4, 1)
Step 1. (−4, −1) ≠ (4, 1) either because −4 ≠ 4 or because −1 ≠ 1.d. 610
5()^62 ,^2 =⎛^6 ,
⎝⎜⎛⎛
⎝⎝⎞
⎠⎟⎞⎞
⎠⎠because 6 = 6 and 210
5=.Quadrants of the Plane
The axes divide the Cartesian coordinate plane into
four quadrants. The quadrants are numbered with
Roman numerals—I, II, III, and IV—beginning
in the upper right and going around counterclock-
wise, as shown in Figure 16.3.
In quadrant I, both coordinates are positive; in quadrant II, the x-coordi-
nate is negative, and the y-coordinate is positive; in quadrant III, both coor-
dinates are negative; and in quadrant IV, the x-coordinate is positive, and
the y-coordinate is negative. Points that have 0 as one or both of the coor-
dinates are on the axes. If the x-coordinate is 0, the point lies on the y-axis.
If the y-coordinate is 0, the point lies on the x-axis. If both coordinates of a
point are 0, the point is at the origin.Don’t forget that the quadrants
are numbered counterclockwise.