Understand Signs in Coordinate Plane - 6th Grade Math

1. Which axis contains all points with $y=0$?

   The $x$-axis. Points with zero $y$-coordinate lie horizontally on the $x$-axis.

2. Which axis is the line of reflection if $(a,b)$ maps to $(a,-b)$?

   The $x$-axis. Only $y$ changes sign, so reflection is across horizontal axis.

3. What is the location name for the point $(0,0)$ on the coordinate plane?

   The origin. The intersection of the $x$ and $y$ axes is called the origin.

4. Which axis contains all points with $x=0$?

   The $y$-axis. Points with zero $x$-coordinate lie vertically on the $y$-axis.

5. Identify the reflection of $(x,y)$ across the $y$-axis.

   $(-x,y)$. Reflecting across $y$-axis changes the sign of $x$ only.

6. What quadrant contains points with $x>0$ and $y<0$?

   Quadrant IV. Positive $x$ and negative $y$ place points in the lower-right quadrant.

7. Identify the quadrant or axis location of the point $(9,0)$.

   On the $x$-axis. When $y=0$, the point lies on the horizontal $x$-axis.

8. Identify the reflection of $(6,-1)$ across both axes (through the origin).

   $(-6,1)$. Reflecting through origin changes both signs: $(6,-1)$ to $(-6,1)$.

9. Identify the quadrant or axis location of the point $(4,-2)$.

   Quadrant IV. Positive $x$ and negative $y$ place this point in the lower-right quadrant.

10. What does a negative $y$-coordinate mean about a point's position relative to the $x$-axis?

    The point is below the $x$-axis. Negative $y$ values are always below the horizontal axis.

11. What do the signs in an ordered pair $(x,y)$ tell you about the point's location on the coordinate plane?

    They tell the directions from the origin: $x$ left/right, $y$ down/up. Positive means right/up from origin; negative means left/down.

12. Identify the reflection of $(x,y)$ across both axes (through the origin).

    $(-x,-y)$. Reflecting through origin changes both signs.

13. What quadrant contains points with $x<0$ and $y<0$?

    Quadrant III. Both coordinates are negative in the lower-left quadrant.

14. What reflection across the $x$-axis does to $(x,y)$ in ordered-pair form?

    $(x,y)\rightarrow(x,-y)$. Reflecting across $x$-axis negates the $y$-coordinate only.

15. What reflection across the $y$-axis does to $(x,y)$ in ordered-pair form?

    $(x,y)\rightarrow(-x,y)$. Reflecting across $y$-axis negates the $x$-coordinate only.

16. What reflection across both axes (through the origin) does to $(x,y)$?

    $(x,y)\rightarrow(-x,-y)$. Reflecting through the origin negates both coordinates.

17. Which quadrant contains the point $(3,-5)$?

    Quadrant IV. Positive $x$ and negative $y$ place it in the lower right.

18. What does a positive $y$-coordinate mean about a point's position relative to the $x$-axis?

    The point is above the $x$-axis. Positive $y$ values are always above the horizontal axis.

19. What are the signs of coordinates for Quadrant III?

    Quadrant III: $(-,-)$. Both coordinates negative means lower left quadrant.

20. Which quadrant contains the point $(3,5)$?

    Quadrant I. Both coordinates are positive, placing it in the upper right.

21. Identify the quadrant or axis location of the point $(0,-8)$.

    On the $y$-axis. When $x=0$, the point lies on the vertical $y$-axis.

22. What is the reflection of $(4,-2)$ across the $x$-axis?

    $(4,2)$. Change sign of $y$: $-2$ becomes $2$, $x$ stays $4$.

23. Identify the quadrant or axis location of the point $(-6,-1)$.

    Quadrant III. Both coordinates are negative, placing it in the lower-left quadrant.

24. Identify the reflection of $(-5,2)$ across the $y$-axis.

    $(5,2)$. Reflecting across $y$-axis changes $x$ from $-5$ to $5$.

25. Identify the reflection of $(3,-4)$ across the $x$-axis.

    $(3,4)$. Reflecting across $x$-axis changes $y$ from $-4$ to $4$.

26. Identify the quadrant or axis location of the point $(-3,5)$.

    Quadrant II. Negative $x$ and positive $y$ place this point in the upper-left quadrant.

27. What does a negative $x$-coordinate mean about a point's position relative to the $y$-axis?

    The point is to the left of the $y$-axis. Negative $x$ values are always left of the vertical axis.

28. Which quadrant contains the point $(-3,-5)$?

    Quadrant III. Both coordinates are negative, placing it in the lower left.

29. What are the signs of coordinates for Quadrant II?

    Quadrant II: $(-,+)$. Negative $x$, positive $y$ means upper left quadrant.

30. What quadrant contains points with $x<0$ and $y>0$?

    Quadrant II. Negative $x$ and positive $y$ place points in the upper-left quadrant.

31. What is the reflection of $(4,-2)$ across both axes?

    $(-4,2)$. Change both signs: $(4,-2)$ becomes $(-4,2)$.

32. What quadrant contains points with $x>0$ and $y>0$?

    Quadrant I. Both coordinates are positive in the upper-right quadrant.

33. Which quadrant contains the point $(-3,5)$?

    Quadrant II. Negative $x$ and positive $y$ place it in the upper left.

34. What does a positive $x$-coordinate mean about a point's position relative to the $y$-axis?

    The point is to the right of the $y$-axis. Positive $x$ values are always right of the vertical axis.

35. Identify the reflection of $(x,y)$ across the $x$-axis.

    $(x,-y)$. Reflecting across $x$-axis changes the sign of $y$ only.

36. What do the signs of $x$ and $y$ in an ordered pair $(x,y)$ tell you on a coordinate plane?

    They tell the quadrant or axis location of the point $(x,y)$. Signs determine which of the four quadrants or two axes the point lies on.

37. What is the reflection of $(4,-2)$ across the $y$-axis?

    $(-4,-2)$. Change sign of $x$: $4$ becomes $-4$, $y$ stays $-2$.

38. What are the signs of coordinates for Quadrant I?

    Quadrant I: $(+,+)$. Both coordinates positive means upper right quadrant.

39. Identify the quadrant or axis location of the point $(2,7)$.

    Quadrant I. Both coordinates are positive, placing it in the upper-right quadrant.

40. What are the signs of coordinates for Quadrant IV?

    Quadrant IV: $(+,-)$. Positive $x$, negative $y$ means lower right quadrant.

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