The coordinates of the point A, where AB is the diameter of the circle whose centre is (3, 2) and B (7, 4) is :

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 $(x_1, y_1)$ and $(x_2, y_2)$, 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 $(x_A, y_A)$. We substitute the coordinates of the center $(3, 2)$ as the midpoint $M$, and the coordinates of point B $(7, 4)$ as $(x_2, y_2)$ 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 $x_A$.

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 $y_A$.

More from this chapter

• Q7. If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B when joined, then establish a relation between a and b. [2 Marks]
• Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by the point (-1, 6).
• Find a point on the y-axis that is at the same distance from the points (-5, 2) and (9, -2).
• Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3:1 internally.
• Find the relation between x and y if the point (x, y) is equidistant from (7, 1) and (3, 5).
• 1. Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (-a, -b)
• Find the coordinates of the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4).
• Find the ratio in which the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis, and find the coordinates of the point of division.

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