Question
The point which lies on \( x \)-axis at a distance of 3 units in the positive direction of \( x \)-axis is \( \begin{array}{ll}\text { a) }(0,-3) & \text { b) }(0,3) \\ \text { c) }(3,0) & \text { d) }(-3,0)\end{array} \)
Ask by Watson Pena. in India
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The point is \( (3, 0) \).
Solution
The point on the \( x \)-axis that is 3 units in the positive direction from the origin can be determined as follows:
- **Location on the \( x \)-axis:** Any point on the \( x \)-axis has the form \( (x, 0) \) because the \( y \)-coordinate is zero.
- **Distance and Direction:** Moving 3 units in the positive \( x \)-direction from the origin \( (0, 0) \) takes you to the point \( (3, 0) \).
**Therefore, the correct answer is:**
**c) \( (3, 0) \)**
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Simplify this solution Bonus Knowledge
The point that lies on the \( x \)-axis at a distance of 3 units in the positive direction of the \( x \)-axis is \((3,0)\), which is option c). On the \( x \)-axis, the \( y \)-coordinate is always zero, so any point on this line will have the form \((x,0)\). In the Cartesian coordinate system, the \( x \)-axis is the line where all \( y \)-values are 0. Therefore, when describing a point that is exactly 3 units to the right of the origin (0,0), you would land at (3,0), demonstrating how the axes help establish clear locations in a two-dimensional space!
