Graph the points on a rectangular coordinate system.
a.
(
1
2
,
5
)
b.
(
−
1
,
4
)
c.
(
2
,
−
1
)
d.
(
0
,
3
)
e.
(
0
,
0
)
f.
(
−
8
5
,
0
)
g.
(
−
2
,
−
5
)
h.
(
3
,
1
)
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
(a)
Expert Solution
To determine
To Graph: The point (12,5) on a rectangular coordinate system.
Explanation of Solution
Given Information:
The point, (12,5).
Graph:
Interpretation:
The ordered pair (12,5) indicates x=12andy=5.
Therefore, the point (12,5) is in Quadrant I.
(b)
Expert Solution
To determine
To Graph: The point (−1,4) on a rectangular coordinate system.
Explanation of Solution
Given Information:
The point, (−1,4).
Graph:
Interpretation:
The ordered pair (−1,4) indicates x=−1andy=4.
Therefore, the point (−1,4) is in Quadrant II.
(c)
Expert Solution
To determine
To Graph: The point (2,−1) on a rectangular coordinate system.
Explanation of Solution
Given Information:
The point, (2,−1).
Graph:
Interpretation:
The ordered pair (2,−1) indicates x=2andy=−1.
Therefore, the point (2,−1) is in Quadrant IV.
(d)
Expert Solution
To determine
To Graph: The point (0,3) on a rectangular coordinate system.
Explanation of Solution
Given Information:
The point, (0,3).
Graph:
Interpretation:
The ordered pair (0,3) indicates x=0andy=3.
Therefore, the point (0,3) indicates that x=0 which implies that the point is on y-axis.
(e)
Expert Solution
To determine
To Graph: The point (0,0) on a rectangular coordinate system.
Explanation of Solution
Given Information:
The point, (0,0).
Graph:
Interpretation:
The ordered pair (0,0) indicates x=0andy=0.
Therefore, the point (0,0) is at the origin.
(f)
Expert Solution
To determine
To Graph: The point (−85,0) on a rectangular coordinate system.
Explanation of Solution
Given Information:
The point, (−85,0).
Graph:
Interpretation:
The ordered pair (−85,0) indicates x=−85andy=0 or x=−1.6andy=0.
Therefore, the point (−85,0) indicates that y=0 which implies that the point is on x-axis.
(g)
Expert Solution
To determine
To Graph: The point (−2,−5) on a rectangular coordinate system.
Explanation of Solution
Given Information:
The point, (−2,−5).
Graph:
Interpretation:
The ordered pair (−2,−5) indicates x=2andy=−5.
Therefore, the point (−2,−5) is in Quadrant III.
(h)
Expert Solution
To determine
To Graph: The point (3,1) on a rectangular coordinate system.
Explanation of Solution
Given Information:
The point, (3,1).
Graph:
Interpretation:
The ordered pair (3,1) indicates x=3andy=1.
Therefore, the point (3,1) is in Quadrant I.
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