Q1: Which of these best describes the coordinate plane? (a) A number line with only positive numbers (b) Two perpendicular number lines that intersect at zero (c) A grid with only vertical lines (d) A ruler used to measure length
Solution:
Ans: (b) Explanation: The coordinate plane is formed by two perpendicular number lines called the x-axis (horizontal) and y-axis (vertical) that intersect at the origin, which is the point \((0, 0)\).
Q2: What is the point where the x-axis and y-axis intersect called? (a) The endpoint (b) The origin (c) The center point (d) The midpoint
Solution:
Ans: (b) Explanation: The point where the x-axis and y-axis meet is called the origin. It has coordinates \((0, 0)\).
Q3: In the ordered pair \((5, 3)\), which number represents the x-coordinate? (a) 3 (b) 5 (c) 8 (d) 15
Solution:
Ans: (b) Explanation: In an ordered pair \((x, y)\), the first number is always the x-coordinate, which tells how far to move horizontally from the origin. The second number is the y-coordinate. So in \((5, 3)\), the x-coordinate is 5.
Q4: If a point is located at \((0, 7)\), where is it on the coordinate plane? (a) On the x-axis (b) On the y-axis (c) At the origin (d) Between both axes
Solution:
Ans: (b) Explanation: When the x-coordinate is 0, the point lies directly on the y-axis. The point \((0, 7)\) is 7 units up from the origin on the y-axis.
Q5: Starting at the origin, you move 4 units to the right and 6 units up. What are the coordinates of your location? (a) \((6, 4)\) (b) \((4, 6)\) (c) \((10, 0)\) (d) \((0, 10)\)
Solution:
Ans: (b) Explanation: Moving right means moving in the positive direction on the x-axis, and moving up means moving in the positive direction on the y-axis. Right 4 units gives x-coordinate of 4, and up 6 units gives y-coordinate of 6, so the point is \((4, 6)\).
Q6: Which ordered pair represents a point that is 3 units to the left of the origin and 2 units down? (a) \((3, 2)\) (b) \((-3, -2)\) (c) \((2, 3)\) (d) \((-2, -3)\)
Solution:
Ans: (b) Explanation: Moving left from the origin means the x-coordinate is negative, and moving down means the y-coordinate is negative. Left 3 units is \(x = -3\), and down 2 units is \(y = -2\), giving the point \((-3, -2)\).
Q7: Point A is at \((2, 5)\) and Point B is at \((2, 9)\). What is true about these two points? (a) They are on the same horizontal line (b) They are on the same vertical line (c) They are the same point (d) They are on different axes
Solution:
Ans: (b) Explanation: When two points have the same x-coordinate, they lie on the same vertical line. Both points have \(x = 2\), so they are vertically aligned, with Point B being 4 units above Point A.
Q8: What is the y-coordinate of any point that lies on the x-axis? (a) 1 (b) Always positive (c) 0 (d) Always negative
Solution:
Ans: (c) Explanation: Any point on the x-axis has not moved up or down from the origin, so its y-coordinate is always 0. Examples include \((5, 0)\), \((-3, 0)\), and \((0, 0)\).
## Section B: Fill in the Blanks Q9: The horizontal number line on a coordinate plane is called the __________.
Solution:
Ans: x-axis Explanation: The x-axis is the horizontal number line on the coordinate plane, while the vertical number line is called the y-axis.
Q10: In the ordered pair \((x, y)\), the second number represents the __________ coordinate.
Solution:
Ans: y Explanation: In any ordered pair, the first number is the x-coordinate and the second number is the y-coordinate.
Q11: The ordered pair that represents the origin is __________.
Solution:
Ans: \((0, 0)\) Explanation: The origin is the point where the x-axis and y-axis intersect, and it has coordinates \((0, 0)\).
Q12: If you move left from the origin on the coordinate plane, the x-coordinate will be __________.
Solution:
Ans: negative Explanation: Moving left from the origin means moving in the negative direction on the x-axis, so the x-coordinate is negative.
Q13: Two points with the same y-coordinate lie on the same __________ line.
Solution:
Ans: horizontal Explanation: When points share the same y-coordinate, they are at the same vertical height, so they lie on the same horizontal line.
Q14: The distance between the points \((3, 5)\) and \((3, 8)\) on the coordinate plane is __________ units.
Solution:
Ans: 3 Explanation: Since both points have the same x-coordinate, they lie on a vertical line. The distance is found by subtracting the y-coordinates: \(8 - 5 = 3\) units.
## Section C: Word Problems Q15: Maya is playing a game on a coordinate grid. She starts at the origin and moves 5 units to the right and then 3 units up. What are the coordinates of her final position?
Solution:
Ans: Final Answer: \((5, 3)\)
Q16: A treasure map shows that a treasure is buried at point \((6, 4)\). If you are currently at the origin, how many units to the right and how many units up do you need to move to reach the treasure?
Solution:
Ans: Final Answer: 6 units to the right and 4 units up
Q17: On a coordinate plane, the library is located at \((2, 7)\) and the school is located at \((2, 3)\). How far apart are the library and school?
Solution:
Ans: Final Answer: 4 units
Q18: A bee starts at point \((4, 5)\) on a coordinate grid. It flies 3 units down. What are the new coordinates of the bee?
Solution:
Ans: Final Answer: \((4, 2)\)
Q19: Jake plotted four points on a coordinate plane: Point A at \((1, 3)\), Point B at \((5, 3)\), Point C at \((5, 6)\), and Point D at \((1, 6)\). If he connects these points in order and then connects Point D back to Point A, what shape does he create?
Solution:
Ans: Final Answer: Rectangle
Q20: A park has a walking path represented on a coordinate plane. The path starts at \((0, 0)\), goes to \((8, 0)\), then to \((8, 5)\), and finally to \((0, 5)\) before returning to the start. What is the total distance walked along this rectangular path?
Solution:
Ans: Final Answer: 26 units
The document Worksheet (with Solutions): Coordinate Plane is a part of the Grade 5 Course Math Grade 5.
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