Positions to the left and below
Distinguish negative directions on both axes and read signed coordinates.
Begin with the activity ↓Does one negative number always mean bottom left?
A negative first value means left; a negative second value means down. Read each sign separately.
Extend the horizontal number line left of the origin: right is positive and left is negative. Extend the vertical axis downward too: above the origin is positive and below it is negative.
For (-2, 3), find two units left because the first number is −2, then three units up because the second is 3. The point is above and left of the origin. One negative sign does not make both directions negative.
The point (2, -3) is two right and three down. The point (-2, -3) is two left and three down. Keep each sign with its value and retain horizontal-then-vertical order.
The axes divide the plane into four regions. For now, explain how each sign determines a direction instead of memorizing region names or numbers. Points on the axes are distinct from points inside those regions.
With the horizontal value fixed, increasing the vertical value moves a point upward. Changing (-2, -3) to (-2, -1) moves it two units up. Increasing values keep the same direction even below zero.
A negative coordinate describes position on the other side of a reference. It does not mean negative length or a negative count of objects. Next we examine zero, which is neither positive nor negative.
Listen one paragraph at a time
Hold on to this distinction
(-3, 1) means three left and one up. (3, -1) means three right and one down. Check which position carries the negative sign.
Change it and check
Hold horizontal fixed and change the vertical sign; then hold vertical fixed and change the horizontal sign. Describe each direction of change.
Right · above
The screen shows integer points from −4 to 4, with a constant unit interval on each axis. Coordinate signs are not used here to calculate travel distance or area.
Try with paper and objects
Draw two crossing axes and mark (-1, 2), (1, -2), and (-1, -2). Describe each point with a horizontal and a vertical direction.
Check and explain another example
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(-2, -1) · two numbers: horizontal, then vertical
Left gives horizontal −2 and down gives vertical −1: (-2, -1).
Does your explanation include these ideas?
Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.
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Distinguish points on the axes from the origin and explain zero.