Find the coordinates of the point A where ab is the diameter of circle whose Centre is A (2, - 3 )and B(1 ,4)
Answers
Please see the attachment
C O N C E P T :
→ This question is easy to solve but it also has places for silly mistakes, like we have to remember that we have to add the x-coordinates of the endpoints and divide by 2 to get the coordinates of the mid-point. We have to do similarly with the y-coordinates too. The formula for x-coordinate of mid-point is x ¹ + x ² / 2 and not x² + -x¹ The same goes for y-coordinate too. This mistake is committed by students when they get confused with the distance formula. So, they just have to check to keep an example in mind, we know the midpoint of 2 and 4 is 3, that is, 2 + 4 / 2 = 6 / 2 = 3 and not 4 - 2 / 2 = 2 / 2 = 1 The mid-point concept is also used for getting the mid-point of diagonals or side’s endpoints of any rectangle or parallelogram.
→ This is a simple question based on the mid-point theorem. In any straight line AB, whose coordinates are A ( x¹ + y¹ ) and B ( x² + y² ) and if the mid-point of AB is C ( x, y ) then x = x¹ + x² / 2 and y = y¹ + y² / 2
S O L U T I O N :
→ Let us assume the coordinate of A as (x,y). Now, as the centre is the mid-point of AB, which is given as (2, -3) and we have the B as (1, 4) , we will apply the mid-point theorem, x = x - ¹ + x ² / 2 And Y = Y ¹ + Y ² / 2 So, we will get,
: x = x 1 + x 2 / 2
: 2 = x + 1 / 2
: 4 = x + 1
: x = 1
Similarly, we will find the value of y also,
: y = y¹ + y ² / 2
: - 3 = y + 4 / 2
: -6 = y + 4
: y = - 10