How can I determine the coordinates of the point that is equidistant from points A (2, 3) and C (5, 6)?

To find the coordinates of the point that is equidistant from points A (2, 3) and C (5, 6), we can utilize the geometric concept of the midpoint of the line segment connecting these two points.

The coordinates of the midpoint (M) can be calculated using the following formula:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Where:

• (x₁, y₁) are the coordinates of point A
• (x₂, y₂) are the coordinates of point C

Substituting the coordinates of points A (2, 3) and C (5, 6) into the formula, we have:

M = ((2 + 5) / 2, (3 + 6) / 2)

Calculating this gives us:

• X-coordinate: (2 + 5) / 2 = 7 / 2 = 3.5
• Y-coordinate: (3 + 6) / 2 = 9 / 2 = 4.5

Therefore, the coordinates of the point that is equidistant from points A and C are:

(3.5, 4.5)

This point, M (3.5, 4.5), is exactly halfway between A and C, making it equidistant from both points.