MATH: UNDERSTANDING THE COORDINATE PLANE
Quick Check

1. What are the coordinates of point A?
A. (-4,3)
B. (3,-4)
C. (-4,4)
D. (-3,4)

2. What are the coordinates of Point B?
A. (1,3)
B. (3,1)
C. (-3,1)
D. (1, -3)
3. Which point is located at (4,-5)?
A. A
B. B
C. C
D. D
4. In which quadrant is Point C?
A. Quadrant 1
B. Quadrant 11
C. Quadrant 111
D. Quadrant 1V

5. If the coordinates of a point have the same sign, which quadrant(s) could the point be in?
A. Quadrants 1 and 11
B. Quadrants 1 and 111
C. Quadrants 111
D. Quadrants 1V

I recreated the coordinate plane with your points and draw the attached image to answer your question with complete explanation.

Here is every question each with its answer and explanation.

1. What are the coordinates of point A?

   A. (-4,3)

   B. (3,-4)

   C. (-4,4)

   D. (-3,4)

Explanation:

In an ordered pair (a,b), the first number, a, is the x-coordinate. Thus, you must imaginally draw a vertical line from the point A to the x-axis and read the corresponding mark. In this case, that mark is to the left of the coordinate origin of the plane, thus it is negative. The value that you will read is -4.

In the same ordered pair (a,b), the second number, b, is the y-coordinate. Thus, you must must imaginally draw a horizontal line from the point A to the y-axis and read the corresponding mark. In this case, that mark above the coordinate origin of the plane, thus it is positive. The value you will read is 3.

Hence, the coordinates of the point A are (4, -3), option A.

2. What are the coordinates of Point B?

   A. (1,3)

   B. (3,1)

  C. (-3,1)

  D. (1, -3)

Explanation:

To find the x-coordinate go, vertically down from the point B until you find the x-axis. Read the mark on the axis. It is to the right of the coordinate origin, thus it is positive. Tha value is 3. Thus, the first number of your ordered pair is 3.

To find the y-coordinate, go horizontally to the left until you find the y-axis. That is above the coordnate origin, thus the coordinate is positive. The corresponding mark that you read is 1. Therefore, the second number of your ordered pair is 4.

Therefore, the coordinates of point B are (3, 1): the option B, from the choices.

3. Which point is located at (4,-5)?

    A. A

   B. B

   C. C

   D. D

Explanation:

Now the work is different. You must start on the axis and then find the point.

The first number of the ordered pair (4, -5) is the x-coordinate and the second number is the y-coordinate.

Then, draw a vertical line through the mark x = 4 (on the x-axis) and a horizontal line through the mark y = - 5 (on the y-axis).

The intersection of those two lines is the point (4, -5) that is the point C on the diagram.

4. In which quadrant is Point C?

   A. Quadrant I

   B. Quadrant II

   C. Quadrant III

   D. Quadrant IV

Explanation

The two perpendicular lines determine 4 sections of the coordinate plane. Those sections are named quadrants are numbered in the counterclockwise.

The point C is in the bottom left secion, thus it is quadrant III,which is the option C.

5. If the coordinates of a point have the same sign, which quadrant(s) could the point be in?

   A. Quadrants  I and II

   B. Quadrants I and III

   C. Quadrants III

   D. Quadrants IV

Explanation:

By the construction, the quadrant I contains the points with positive x-coordinates and positive y-coordinates. Thus, the coordinates of a point on the quadrant I are both equal (positive).

Also, the quadrant III contains the points with negative x-coordinates and negative y-coordinates. Thus, the coordinates of a point on the quadrant III are both equal (negative).

Therefore, both quadrants I and III could be the quadrants where the point whose coordinates have the same sign is. Thus, the option B. Quadrants I and III is true.

On the other hand, the other two quadrants can only contain points whose coordinates have opposite signs.