Questions: Coordinate Plane — All Four Quadrants

Question 1

A student is told to plot the point (−4, 7). She counts 7 units to the left and 4 units up, then marks her point. What error did she make?

• A. She moved in the wrong vertical direction — 7 should be downward
• B. She reversed the x and y coordinates — she should have moved 4 units left and 7 units up
• C. She was correct — (−4, 7) means 7 left and 4 up
• D. She forgot to start from the origin

Answer: (B)

In an ordered pair (x, y), the x-coordinate always comes first and describes horizontal movement; the y-coordinate is second and describes vertical movement. For (−4, 7), you move 4 units left (because x = −4 is negative) and then 7 units up (because y = 7 is positive). She swapped the roles of the two values — the most common error in early coordinate work.

Question 2

Where is the point (0, −5) located on the coordinate plane?

• A. In Quadrant III, because the y-coordinate is negative
• B. In Quadrant IV, because x is zero and y is negative
• C. On the y-axis, not in any quadrant
• D. At the origin, because x is zero

Answer: (C)

Points with x = 0 lie on the y-axis, and points with y = 0 lie on the x-axis. Points on either axis are not in any quadrant — the quadrants are the four interior regions. The point (0, −5) is 5 units below the origin on the y-axis. A common misconception is to assign axis points to an adjacent quadrant based on the sign of their nonzero coordinate, but axes are boundaries between quadrants, not part of them.

Question 3

The ordered pair (3, 7) and the ordered pair (7, 3) represent the same point on the coordinate plane.

• T. True
• F. False

Answer: False

The word 'ordered' in ordered pair is essential — the position of each number matters. (3, 7) means 3 units right and 7 units up. (7, 3) means 7 units right and 3 units up. These are completely different locations. The x-coordinate always comes first (think: x before y, horizontal before vertical). This is one of the most common early errors in coordinate graphing.

Question 4

In Quadrant II of the coordinate plane, the x-coordinate is always negative and the y-coordinate is always positive.

• T. True
• F. False

Answer: True

Quadrant II is in the upper-left region: left of the y-axis (negative x) and above the x-axis (positive y). The sign patterns for all four quadrants are: Quadrant I (+, +), Quadrant II (−, +), Quadrant III (−, −), Quadrant IV (+, −), numbered counterclockwise from the upper right. Knowing these sign patterns lets you quickly sanity-check whether a plotted point is in the right quadrant.

Question 5

Why does the order of coordinates in an ordered pair matter? What goes wrong if you swap the x and y values?

Model answer: The x and y coordinates each describe movement along a specific axis — x is horizontal, y is vertical. Swapping them means moving the wrong distance along the wrong axis, landing you at a completely different location. For example, (3, 7) places you 3 right and 7 up; (7, 3) places you 7 right and 3 up — different points entirely. The 'ordered' in ordered pair means the position within the pair encodes meaning, not just the numbers themselves.

This is why the convention 'x always comes first' is so important to memorize. The coordinate plane is an address system, and swapping coordinates is like transposing the house number and the street name — you end up at the wrong place. As students move into graphing equations, getting coordinates in the right order is what makes solution pairs map correctly to points on the line.