Coordinate Geometry and Graphs quiz featuring multiple-choice questions on Cartesian coordinate system, axes, quadrants, and line relationships.

Let's solve each question in the worksheet "Coordinate Geometry and Graphs" step by step with explanations.

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1. The horizontal number line of a Cartesian coordinate system is called _________.

- Answer: a. x-axis
✔ Explanation: In the Cartesian plane, the horizontal axis is known as the x-axis.

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2. The vertical number line of a Cartesian coordinate system is called _________.

- Answer: b. y-axis
✔ Explanation: The vertical axis is called the y-axis.

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3. Both the axes are perpendicular to each other, that is they meet in a _________.

- Answer: b. Right angle
✔ Explanation: The x-axis and y-axis intersect at 90 degrees, which is a right angle.

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4. The point of intersection of both axes is called _________.

- Answer: d. Origin
✔ Explanation: The point where the x-axis and y-axis intersect is called the origin, denoted as (0, 0).

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5. The Cartesian plane is also called _________.

- Answer: a. Rectangular Plane
✔ Explanation: The Cartesian plane is also referred to as the rectangular coordinate plane because it uses perpendicular axes.

> Note: "xy-plane" is correct too, but since "Rectangular Plane" is listed and commonly used, it's acceptable here. However, both a and b could be argued. But in standard terminology, a. Rectangular Plane is more general and accurate.

But let’s check:
- b. xy-plane – technically correct, but usually refers to the plane in 3D space.
- a. Rectangular Plane – is an alternate name for Cartesian plane.

So a is best.

✔ Answer: a. Rectangular Plane

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6. x-axis and y-axis divides the Cartesian plane into _________ quadrants.

- Answer: d. four
✔ Explanation: The two axes divide the plane into four quadrants.

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7. In Quadrant I:

- Answer: a. x > 0, y > 0
✔ Explanation: In Quadrant I, both x and y coordinates are positive.

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8. In Quadrant II:

- Answer: c. x < 0, y > 0
✔ Explanation: In Quadrant II, x is negative and y is positive.

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9. In Quadrant III:

- Answer: d. x < 0, y < 0
✔ Explanation: Both x and y are negative in this quadrant.

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10. In Quadrant IV:

- Answer: b. x > 0, y < 0
✔ Explanation: x is positive, y is negative.

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11. The point (3, -4) is located in

- Answer: d. Quadrant IV
✔ Explanation: x = 3 (>0), y = -4 (<0) → Quadrant IV

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12. The two coordinate axes intersect at an angle of

- Answer: c. 90°
✔ Explanation: The x-axis and y-axis are perpendicular, so they intersect at 90 degrees.

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13. The lines represented by the equations x + y = 3 and x + y = 2 are

- Answer: a. Parallel
✔ Explanation: Both lines have the same slope (slope = -1), but different y-intercepts. So they are parallel and never intersect.

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14. The line y = a where a is a real number is parallel to

- Answer: a. x-axis
✔ Explanation: A line of the form y = a is a horizontal line, which is parallel to the x-axis.

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15. The solution set of the lines x = 1 and x = 2 is

- Answer: d. { }
✔ Explanation:
- x = 1 is a vertical line passing through x = 1.
- x = 2 is a vertical line passing through x = 2.
These lines are parallel and never intersect.
So, there is no common point → No solution.

Hence, the solution set is empty: { }

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## ✔ Final Answers:

| Q# | Answer |
|----|--------|
| 1 | a. x-axis |
| 2 | b. y-axis |
| 3 | b. Right angle |
| 4 | d. Origin |
| 5 | a. Rectangular Plane |
| 6 | d. four |
| 7 | a. x > 0, y > 0 |
| 8 | c. x < 0, y > 0 |
| 9 | d. x < 0, y < 0 |
| 10 | b. x > 0, y < 0 |
| 11 | d. Quadrant IV |
| 12 | c. 90° |
| 13 | a. Parallel |
| 14 | a. x-axis |
| 15 | d. { } |

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