How to graph an ordered pair

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ACT Math › How to graph an ordered pair

Questions 1 - 10
1

Which pair of coordinates lies within quadrant II?

Explanation

By definition, quadrant I has positive coordinates, quadrant II has coordinates, quadrant III has negative coordinates, and quadrant IV has coordinates, as shown by the diagram below. Only one answer choice falls within quadrant II. All others lie in other coordinates or one of the axes.

Quadrants

- Quadrant II

- Quadrant I

- x-axis

- y-axis

- Quadrant III

2

Which point best represents the coordinates ?

Picture1

A

B

C

D

Explanation

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

To get to , move left on the x-axis by , then move up on the y-axis by .

3

Which point best represents the coordinate ?

Picture3

C

A

B

D

Explanation

To get to , move right on the x-axis by then move up on the y-axis by .

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

4

Which point best represents the coordinate ?

Picture6

B

A

C

D

Explanation

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis. The first term in the ordered pair is the movement in the x direction and the second point is the movement in the y direction.

To get to , only move right on the x-axis by .

5

Which point best represents the coordinate ?

Picture5

B

A

C

D

Explanation

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

To get to , move right on the x-axis by , then move down on the y-axis by .

6

Coordinate_pair_1

What are the coordinates of Point A, and in which quadrant is it located?

, Quadrant IV

, Quadrant II

, Quadrant IV

, Quadrant II

Explanation

Coordinate points are given x-coordinate first, y-coordinate second. Quadrants are numbered counter-clockwise, with Quadrant I consisting of positive x-coordinates and positive y-coordinates, Quadrant II consisting of negative x-coordinates and positive y-coordinates, Quadrant III consisting of negative x-coordinates and negative y-coordinates, and Quadrant IV consisting of positive x-coordinates and negative y-coordinates.

(3, -2), Quadrant IV is correct because it lists the coordinates in the correct order and correctly identifies the Quadrant.

(3, -2), Quadrant II is incorrect because, while it lists the coordinates in the correct order, it misidentifies the Quadrant.

(-2, 3), Quadrant IV is incorrect because, while it correctly identifies the Quadrant, it lists the coordinates in the incorrect order.

(-2, 3), Quadrant II is incorrect because it both lists the coordinates in the incorrect order and misidentifies the Quadrant.

7

In the standard xy coordinate plane, what quadrant(s) could point A lie in, if its x-coordinate and y-coordinate have opposite signs?

Quadrant II

Quadrants I and III

Quadrant III

Quadrants II and IV

Quadrants IV

Explanation

We know that right of the origin represents the positive x-direction, and above the origin represents the positive y-direction. For Quadrant I, both the x-coordinate and y-coordinate must be positive, i.e. (+,+). For quadrant II, the x-coordinate is negative, while the y-coordinate is positive, i.e. (+, -). For Quadrant III, both coordinates must be negative, i.e. (-, -). For Quadrant IV, the x-coordinate is positive, and the y-coordinate is negative, i.e. (+, -).

8

Which point best represents the coordinate ?

Picture10

C

A

B

D

Explanation

To get to , move left on the x-axis by , then down on the y-axis by .

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis. The first term in the ordered pair is the movement in the x direction and the second point is the movement in the y direction.

9

Which point best represents the coordinate ?

Picture8

D

A

B

C

Explanation

To get to , move right along the x-axis by , then move up on the y-axis by .

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

10

Which point best represents the coordinate ?

Picture7

B

A

C

D

Explanation

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

To get to , move right on the x-axis by then move down on the y-axis by .

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