To find the point on the y-axis that is equidistant from the points [tex]\((7, 6)\)[/tex] and [tex]\((-3, 4)\)[/tex], you follow the steps below:
1. Identify the Coordinates:
- The coordinates of point A are [tex]\((7, 6)\)[/tex].
- The coordinates of point B are [tex]\((-3, 4)\)[/tex].
2. Determine the Midpoint's y-coordinate:
- To find the y-coordinate of a point on the y-axis equidistant from both points A and B, you need to find the average of the y-coordinates of the given points.
- The y-coordinate of point A is [tex]\(6\)[/tex].
- The y-coordinate of point B is [tex]\(4\)[/tex].
3. Calculate the Average (Midpoint) y-coordinate:
- [tex]\[ \text{Midpoint y-coordinate} = \frac{6 + 4}{2} = \frac{10}{2} = 5 \][/tex]
4. Determine the x-coordinate:
- Since the point lies on the y-axis, its x-coordinate is [tex]\(0\)[/tex].
5. Form the Equidistant Point:
- The point on the y-axis that is equidistant from [tex]\((7, 6)\)[/tex] and [tex]\((-3, 4)\)[/tex] is [tex]\((0, 5)\)[/tex].
Thus, the point on the y-axis that is equidistant from [tex]\((7, 6)\)[/tex] and [tex]\((-3, 4)\)[/tex] is [tex]\((0, 5)\)[/tex].
