(a) Find the relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5).
OR
(b) Find the coordinates of the points of trisection of the line segment joining the points A(2, -2) and B( -7, 4).
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Step-by-Step Solution
Step 1: Understand the problem
The problem asks for the relation between x and y such that point P(x, y) is equidistant from points A(7,1) and B(3,5). This means the distance from P to A is equal to the distance from P to B.
Step 2: 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. Since PA=PB, we can square both sides to eliminate the square root, giving PA2=PB2.
Step 3: Expand and simplify the equation
Expand the squared terms on both sides of the equation. (a−b)2=a2−2ab+b2 is used for each term. Then, we combine the constant terms.
Step 4: Rearrange and solve for the relation
Cancel out x2 and y2 from both sides. Then, move all x and y terms to one side and constant terms to the other side. Simplify the equation by dividing by a common factor to get the final relation.