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Write the coordinates of a point:

i) Above the [tex]$x$[/tex]-axis, lying on the [tex]$y$[/tex]-axis and at a distance of 6 units.

ii) Lying on the [tex]$x$[/tex]-axis to the left of the origin and at a distance of 3 units.

Sagot :

GinnyAnsweridn
Certainly! Let's address each part of the question step-by-step:

### i) Above the [tex]\( x \)[/tex]-axis, lying on the [tex]\( y \)[/tex]-axis, and at a distance of 6 units

1. Understanding the constraints:
- The point is above the [tex]\( x \)[/tex]-axis. This means its [tex]\( y \)[/tex]-coordinate is positive.
- The point is lying on the [tex]\( y \)[/tex]-axis. This means its [tex]\( x \)[/tex]-coordinate is 0.

2. Distance to the origin:
- The point is 6 units away from the origin.
- Since the point is on the [tex]\( y \)[/tex]-axis and 6 units above the origin, its coordinates are [tex]\((0, 6)\)[/tex].

So, the coordinates of the point are [tex]\((0, 6)\)[/tex].

### ii) Lying on the [tex]\( x \)[/tex]-axis to the left of the origin and at a distance of 3 units

1. Understanding the constraints:
- The point lies on the [tex]\( x \)[/tex]-axis. This means its [tex]\( y \)[/tex]-coordinate is 0.
- The point is to the left of the origin. This means its [tex]\( x \)[/tex]-coordinate is negative.

2. Distance to the origin:
- The point is 3 units away from the origin.
- Since it is to the left of the origin and on the [tex]\( x \)[/tex]-axis, the coordinates of the point are [tex]\((-3, 0)\)[/tex].

So, the coordinates of the point are [tex]\((-3, 0)\)[/tex].

### Summary
- For part i), the coordinates of the point are [tex]\((0, 6)\)[/tex].
- For part ii), the coordinates of the point are [tex]\((-3, 0)\)[/tex].

Here are the coordinates for both points:
1. [tex]\((0, 6)\)[/tex]
2. [tex]\((-3, 0)\)[/tex]

These accurately describe the points as per the conditions given in the question.
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