Find The Harmonic Conjugates Of The Point R(5, 1) With Respect To The Points P(2, 10) And Q(6, –2).

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Question

Find the harmonic conjugates of the point R(5, 1) with respect to the points P(2, 10) and Q(6, –2).

Solution

Correct option is

R(5, 1) is S(8, –8)

 

Let S(α, β) be the harmonic conjugates of the point R(5, 1). Suppose R divides PQ in the ratio λ : 1 internally then S dividesPQ in the ratio λ : 1 externally then 

                          

      

  

Also, 

        

      

  

Now, 

     

and, 

      

Hence harmonic conjugates of R(5, 1) is S(8, –8).

Testing

SIMILAR QUESTIONS

Q1

Find the circumcentre of the triangle whose vertices are (–2, –3), (–1, 0) and (7, –6). Also find the radius of the circumcircle.

Q2

Find the coordinates of the point which divides the line segment joining the points (5, –2) and (9, 6) in the ratio 3 : 1.

Q3

Find the length of median through A of a triangle whose vertices are A(–1, 3), B(1, – 1)and C(5, 1).

Q4

Determine the ratio in which y – x + 2 = 0 divides the line joining (3, –1) and (8, 9).

Q5

The coordinates of three consecutive vertices of a parallelogram are (1, 3), (–1, 2) and (2, 5). Then find the coordinates of the fourth vertex.

Q6

The mid points of the sides of a triangle are (1, 2), (0, –1) and (2, –1). Find the coordinates of the vertices of a triangle with the help of two unknowns.

Q7

Find the coordinates of a point which divides externally the line joining (1, –3) and (–3, 9) in the ratio 1: 3.

Q8

The line segment joining A(6, 3) to B(–1, –4) is doubled in length by having its length added to each end. Find the coordinates of the new ends.

Q9

Find the ratio in which the point (2, y) divides the line segment joining (4, 3) and (6, 3) and hence find the value of y.

Q10

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.