The coordinates of the point A, where AB is the diameter of the circle whose centre is (3, 2) and B (7, 4) is :
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Step-by-Step Solution
Step 1: Understand the relationship between center, diameter, and endpoints
The center of a circle is always the midpoint of its diameter. We are given the coordinates of the center and one endpoint of the diameter. We need to find the coordinates of the other endpoint.
Step 2: Recall the midpoint formula
The midpoint formula states that for two points (x1,y1) and (x2,y2), their midpoint M is given by the average of their respective coordinates.
Step 3: Substitute known values into the midpoint formula
Let the coordinates of point A be (xA,yA). We substitute the coordinates of the center (3,2) as the midpoint M, and the coordinates of point B (7,4) as (x2,y2) into the midpoint formula.
Step 4: Solve for the x-coordinate of A
To find the x -coordinate of A, we equate the x -coordinate of the center to the x -component of the midpoint formula and solve for xA.
Step 5: Solve for the y-coordinate of A
Similarly, to find the y -coordinate of A, we equate the y -coordinate of the center to the y -component of the midpoint formula and solve for yA.