Co­ordinate Geometry Exercise 14.1 (Part-15) | Extra Documents, Videos & Tests for Class 10 PDF Download

Question 56: If P (2, p) is the mid-point of the line segment joining the points A (6, −5) and B (−2, 11). find the value of p.

Answer : 

It is given that mid-point of line segment joining A (6,−5) and B (−2, 11) is

In general to find the mid-point of two pointsand we use section formula as,

So,

Now equate the y component to get,

Question 57: If A (1, 2) B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.

Answer :

Let ABCD be a parallelogram in which the co-ordinates of the vertices are A (1, 2);

B (4, 3) and C (6, 6). We have to find the co-ordinates of the forth vertex.

Let the forth vertex be

Since ABCD is a parallelogram, the diagonals bisect each other. Therefore the mid-point of the diagonals of the parallelogram will coincide.

Now to find the mid-point of two pointsand we use section formula as,

The mid-point of the diagonals of the parallelogram will coincide.

So,

Therefore,

Now equate the individual terms to get the unknown value. So,

Similarly,

So the forth vertex is

Question 58: What is the distance between the points A(sinθ−cosθ,0)Asinθ-cosθ,0 and B(0,sinθ+cosθ)B0,sinθ+cosθ? 

Answer : The given points are A(sinθ−cosθ,0)Asinθ-cosθ,0 and B(0,sinθ+cosθ)B0,sinθ+cosθ.
Using distance formula, we have

       (sin2θ+cos2θ=1) 

Thus, the distance between the given points is √2 units.