Final Answer:
To demonstrate that point A is equidistant from the endpoints of segment BC, we need to prove that the distances from point A to both endpoints, B and C, are equal. Mathematically, this can be expressed as |AB| = |AC|, where |AB| represents the distance between points A and B, and |AC| represents the distance between points A and C.
Step-by-step explanation:
Firstly, let's denote the coordinates of points B, C, and A in a Cartesian coordinate system as (xB, yB), (xC, yC), and (xA, yA) respectively. The distance between two points (x1, y1) and (x2, y2) in a Cartesian plane is given by the distance formula:
Now, we want to prove that |AB| = |AC|. Using the distance formula, we can express this as:
Squaring both sides of the equation eliminates the square root:
Expanding and simplifying both sides should lead to an expression that demonstrates the equality of the distances. If the two sides are equal, it confirms that point A is equidistant from the endpoints of segment BC.