Position Rational Numbers on Diagrams - 6th Grade Math

1. Identify the location of the point $(0,-3)$.

   On the $y$-axis, $3$ units below the origin. $x=0$ means on $y$-axis; $y=-3$ means 3 units down.

2. Identify the point: move $4$ units left and $5$ units up from the origin.

   $(-4,5)$. Left is negative $x$, up is positive $y$.

3. In an ordered pair $(x,y)$, which coordinate tells left or right position on the plane?

   The $x$-coordinate. First coordinate controls horizontal position.

4. Which point lies on the $x$-axis: $(3,\ 0)$ or $(0,\ 3)$?

   $(3,\ 0)$. Points on the $x$-axis have $y=0$, so $(3, 0)$ lies on the $x$-axis.

5. Which number is greater on a number line: $-3$ or $-5$?

   $-3$. $-3$ is to the right of $-5$ on the number line.

6. Which axis contains all points of the form $(0,y)$?

   The $y$-axis. Points with $x=0$ lie on the vertical axis.

7. Identify the correct order from least to greatest: $-1,\ 0,\ -3,\ 2$.

   $-3,\ -1,\ 0,\ 2$. Order negative numbers by magnitude, then place positives after zero.

8. Which quadrant contains the point $(4,-1)$?

   Quadrant IV. Quadrant IV has positive $x$ and negative $y$.

9. What is the opposite of a number $a$ on a number line?

   $-a$. The opposite of any number $a$ is its negative, which equals $-a$.

10. Which number is farther right on a number line: $-3$ or $2$?

    $2$. Positive numbers are always right of negative numbers.

11. Which point is higher on a vertical number line: $-2$ or $4$?

    $4$. Positive numbers are always higher than negative numbers on vertical lines.

12. What are the coordinates of the origin on the coordinate plane?

    $(0,0)$. The origin is where both axes intersect.

13. What are the coordinates of the point on the $y$-axis with $y=-4$?

    $(0,\ -4)$. Points on the $y$-axis have $x=0$, so the coordinates are $(0, -4)$.

14. What is the value of the point halfway between $-4$ and $2$ on a number line?

    $-1$. Average the endpoints: $\frac{-4+2}{2} = -1$.

15. What does it mean for a number to be to the right of another number on a number line?

    It is greater: if $a$ is right of $b$, then $a>b$. Numbers increase from left to right on horizontal number lines.

16. What does absolute value represent on a number line?

    Distance from $0$. Absolute value measures how far a number is from zero.

17. Identify the quadrant for the point $(-4,5)$.

    Quadrant $II$. Quadrant II has negative $x$ and positive $y$.

18. Identify the point farther from $0$: $-\frac{7}{3}$ or $\frac{5}{2}$.

    $\frac{5}{2}$. $|-\frac{7}{3}| = \frac{7}{3} \approx 2.33$ and $|\frac{5}{2}| = 2.5$, so $\frac{5}{2}$ is farther.

19. What point is at the origin of the coordinate plane?

    $(0,\ 0)$. The origin is where both axes intersect, at coordinates zero, zero.

20. Identify the point with $x=-2$ and $y=5$ in ordered-pair form.

    $(-2,\ 5)$. Write coordinates as an ordered pair with $x$ first, then $y$.

21. Identify the quadrant for the point $(2,-7)$.

    Quadrant $IV$. Quadrant IV has positive $x$ and negative $y$.

22. Which quadrant contains the point $(-2,3)$?

    Quadrant II. Quadrant II has negative $x$ and positive $y$.

23. In an ordered pair $(x,y)$, which coordinate tells up or down position on the plane?

    The $y$-coordinate. Second coordinate controls vertical position.

24. Identify the correct order from least to greatest: $-1$, $0$, $-2$, $3$.

    $-2, -1, 0, 3$. Arrange from smallest (most negative) to largest.

25. Which axis contains points with $y=0$?

    The $x$-axis. Points on horizontal axis have zero vertical displacement.

26. What is the correct coordinate format for a point on the coordinate plane?

    $(x,\ y)$. Ordered pairs always list the $x$-coordinate first, then $y$-coordinate.

27. What is the $x$-coordinate of a point in the coordinate plane?

    The horizontal value (left or right). First coordinate shows position along horizontal axis.

28. Which quadrant contains the point $(-3,\ -2)$?

    Quadrant $\mathrm{III}$. Both coordinates are negative, placing the point in the third quadrant.

29. Which axis contains points with $x=0$?

    The $y$-axis. Points on vertical axis have zero horizontal displacement.

30. What number is exactly halfway between $-2$ and $6$ on a number line?

    $2$. The midpoint formula gives $\frac{-2+6}{2} = \frac{4}{2} = 2$.

31. What is the absolute value of $-\frac{5}{2}$?

    $\frac{5}{2}$. Absolute value removes the negative sign, giving the positive value.

32. Where is $1.25$ located on a number line relative to $1$ and $2$?

    Between $1$ and $2$. $1.25 = 1\frac{1}{4}$, which is one-fourth past $1$.

33. In an ordered pair $(x,y)$, which coordinate is written first?

    The $x$-coordinate. Standard notation always lists $x$ before $y$.

34. What is the $y$-coordinate of a point in the coordinate plane?

    The vertical value (up or down). Second coordinate shows position along vertical axis.

35. Which number is farther left on a number line: $-7$ or $-2$?

    $-7$. Smaller negative numbers are farther left.

36. Which point is farther right: $(-1,2)$ or $(3,2)$?

    $(3,2)$. Compare $x$-coordinates: $3>-1$, so $(3,2)$ is farther right.

37. What is the ordered pair for a point with $x=3$ and $y=-2$ on the coordinate plane?

    $(3,-2)$. Write coordinates as $(x,y)$ in that order.

38. Which is closer to $0$ on a number line: $-\frac{3}{4}$ or $\frac{2}{3}$?

    $\frac{2}{3}$. $\frac{2}{3} \approx 0.67$ is closer to $0$ than $|-\frac{3}{4}| = 0.75$.

39. What does a positive number mean on a vertical number line?

    A value located above $0$. Positive numbers are positioned above zero on vertical number lines.

40. Identify the point halfway between $-2$ and $4$ on a number line.

    $1$. Average the endpoints: $\frac{-2+4}{2}=\frac{2}{2}=1$.

41. Which point is farther right on a number line: $-3$ or $-5$?

    $-3$. On a number line, $-3$ is closer to zero than $-5$, so it's farther right.

42. Which axis contains all points of the form $(x,0)$?

    The $x$-axis. Points with $y=0$ lie on the horizontal axis.

43. Which number is farther to the left on a number line: $-1$ or $2$?

    $-1$. Negative numbers are left of zero; positive numbers are right.

44. Identify the location of the point $(5,0)$.

    On the $x$-axis, $5$ units right of the origin. $y=0$ means on $x$-axis; $x=5$ means 5 units right.

45. What does a negative number mean on a horizontal number line?

    A value located to the left of $0$. Negative numbers are positioned left of zero on horizontal number lines.

46. What does it mean for a number to be above another number on a vertical number line?

    It is greater: if $a$ is above $b$, then $a>b$. Numbers increase from bottom to top on vertical number lines.

47. Identify the point: move $3$ units right and $2$ units down from the origin.

    $(3,-2)$. Right is positive $x$, down is negative $y$.

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