ACT Math : How to graph a point

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Graph A Point

How would you plot the point \displaystyle (2,3)?

Possible Answers:

From the origin, go left \displaystyle 2 units, and up \displaystyle 3 units

From the origin, go right \displaystyle 2 units, and up \displaystyle 3 units

From the origin, go right \displaystyle 2 units, and down \displaystyle 3 units

From the origin, go up \displaystyle 2 units, and right \displaystyle 3 units

Correct answer:

From the origin, go right \displaystyle 2 units, and up \displaystyle 3 units

Explanation:

For the ordered pair \displaystyle (2,3)

The first number is for the x-axis, so because it is positive you go right \displaystyle 2.

The second number is for the y-axis, so because it is positive you go up \displaystyle 3.

Example Question #2 : How To Graph A Point

How would you plot the point \displaystyle (-3,5)?

Possible Answers:

From the origin, go right \displaystyle 3 units, and up \displaystyle 5 units

 

From the origin, go left \displaystyle 3 units, and up \displaystyle 5 units

 

From the origin, go right \displaystyle 3 units, and down \displaystyle 5 units

 

From the origin, go left \displaystyle 3 units, and down \displaystyle 5 units

 

Correct answer:

From the origin, go left \displaystyle 3 units, and up \displaystyle 5 units

 

Explanation:

For the ordered pair \displaystyle (-3,5) we would do the following.

The first number is for the x-axis, so because it is negative you go left \displaystyle 3 units.

The second number is for the y-axis, so because it is positive you go up \displaystyle 5 units.

Example Question #2 : How To Graph A Point

In which Quadrant is the point \displaystyle (-3, -3) located?

Possible Answers:

Quadrant III

Quadrant I

Quadrant II

Quadrant IV

Correct answer:

Quadrant III

Explanation:

To find out which quadrant a point lives in, we need to remember the qualities of each quadrant. By qualities, I mean the signs associated with the x and y values which are dependent on the quadrant the point resides in.

All coordinate pairs that are in Quadrant I will have a positive x value and a positive y value.

All coordinate pairs that are in Quadrant II will have a negative x value and a positive y value.

All coordinate pairs that are in Quadrant III will have a negative x value and a negative y value.

All coordinate pairs that are in Quadrant IV will have a positive x value and a negative y value.

For the point \displaystyle (-3, -3) we see that both the x and y values are negative therefore, the point lies in the third quadrant. We can also check this by starting from the origin and going left 3 units and down 3 units. This will end up in the lower-left section of the coordinate-plane, which is Quadrant III.

Example Question #1 : How To Graph A Point

What are the coordinates of point B?

Graph1

Possible Answers:

\displaystyle (2, 4)

\displaystyle (-2, 4)

\displaystyle (4,2)

\displaystyle (4, -2)

Correct answer:

\displaystyle (2, 4)

Explanation:

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is \displaystyle 2.

Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is \displaystyle 4.

\displaystyle (2,4) is then the coordinate of the point.

Example Question #2 : How To Graph A Point

What are the coordinates for point A?

Graph2

Possible Answers:

\displaystyle (6, -2)

\displaystyle (6, 2)

\displaystyle (2, 6)

\displaystyle (-2, 6)

Correct answer:

\displaystyle (2, 6)

Explanation:

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is \displaystyle 2.

Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is \displaystyle 6.

\displaystyle (2, 6) are the coordinates for point A.

Example Question #1 : How To Graph A Point

What are the coordinates for point C?

Graph3

Possible Answers:

\displaystyle (4, 2)

\displaystyle (-4, -2)

\displaystyle (-2, -4)

\displaystyle (2, -4)

Correct answer:

\displaystyle (-4, -2)

Explanation:

Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is \displaystyle -4.

Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is \displaystyle -2.

\displaystyle (-4, -2) are the coordinates for point C.

Example Question #3 : How To Graph A Point

What are the coordinates for point D?

Graph4

Possible Answers:

\displaystyle (-4, 4)

\displaystyle (4, -4)

\displaystyle (-4, -4)

\displaystyle (4, 4)

Correct answer:

\displaystyle (-4, 4)

Explanation:

Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is \displaystyle -4.

Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is \displaystyle 4.

\displaystyle (-4, 4) are the coordinates for point D.

Example Question #371 : Geometry

What are the coordinates for point E?

Graph5

Possible Answers:

\displaystyle (-2, 2)

\displaystyle (-2, -2)

\displaystyle (2, -2)

\displaystyle (2, 2)

Correct answer:

\displaystyle (2, -2)

Explanation:

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is \displaystyle 2.

Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is \displaystyle -2.

\displaystyle (2, -2) are the coordinates for point E.

Example Question #601 : Ssat Upper Level Quantitative (Math)

What are the coordinates for point F?

Graph6

Possible Answers:

\displaystyle (-4, 6)

\displaystyle (4, 6)

\displaystyle (-4, -6)

\displaystyle (-6, -4)

Correct answer:

\displaystyle (-4, -6)

Explanation:

Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is \displaystyle -4.

Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is \displaystyle -6.

\displaystyle (-4, -6) are the coordinates for point F.

Example Question #3 : How To Graph A Point

What are the coordinates for point G?

Graph7

Possible Answers:

\displaystyle (-3, -2)

\displaystyle (-2, -3)

\displaystyle (3, 2)

\displaystyle (2, 3)

Correct answer:

\displaystyle (2, 3)

Explanation:

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is \displaystyle 2.

Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is \displaystyle 3.

\displaystyle (2, 3) are the coordinates for point G.

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