Q1 of 39 Page 1

Find the coordinates of a point A, where AB is a diameter of a circle with centre (-2,2) and B is the point (3, 4).


Let O be the centre of AB.


Since AB is the diameter, so O is the midpoint of AB.


By section formula which states that if a point P (x , y) divides the line with end points A(x1,y1) and B(x2,y2) in the ration m:n, the coordinates of x and y are:




As midpoint divides the line in the ratio 1:1,


Then, the coordinates of A (x, y) can be calculated as:



⇒ a + 3 = 2(-2)


⇒ a + 3 = -4


⇒ a = -7


And,



⇒ b + 4 = 2(2)


⇒ b + 4 = 4


⇒ b = 0


Hence, coordinate of point A is (-7,0).


More from this chapter

All 39 →
29

Prove that in a right-angle triangle the square of the hypotenuse is equal the sum of squares of the other two sides.


 30

If the median of the following frequency distribution is 32.5. Find the values of f1 and f2.

Or


The marks obtained by 100 students of a class in an examination are given below.



Draw ‘a less than’ type cumulative frequency curves (orgive). Hence find median.

 7

find the value of k for which the following pair of linear equations have infinitely many solutions.

2x + 3y = 7


(k+1)x + (2k-1)y = 4k + 1


 13

The arithmetic mean of the following frequency distribution is 53. Find the value of k.