The coordinates of a point on the x-axis, which is equidistant from ( - 2, 5) and (2, - 3) are :
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Step-by-Step Solution
Step 1: Define the point on the x-axis
Let the point on the x -axis be P. Since it lies on the x -axis, its y -coordinate must be 0. So, we can represent the point as (x,0).
Step 2: Set up the distance equation
Let the given points be A(−2,5) and B(2,−3). The problem states that point P is equidistant from A and B. This means the distance from P to A is equal to the distance from P to B.
Step 3: Apply the distance formula
We use the distance formula, which states that the distance between two points (x1,y1) and (x2,y2) is (x2−x1)2+(y2−y1)2. We will apply this formula for PA and PB.
Step 4: Substitute coordinates and solve for x
Substitute the coordinates of P(x, 0), A(−2,5), and B(2,−3) into the distance formula. Square both sides to eliminate the square roots. Then, expand and simplify the equation to solve for x. The x2 terms cancel out, leading to a linear equation.
Step 5: State the coordinates of P
Since we found x=−2, the coordinates of the point P on the x -axis that is equidistant from the given points are (−2,0).