Question 1: Find the mid-point of the line segment joining the points :

Answer:

i) Ratio for being a midpoint:

Let the coordinates of the point

Therefore

ii) Ratio for being a midpoint:

Let the coordinates of the point

Therefore

Question 2: Points have co-ordinates respectively. The mid-point of is .Find the values of

Answer:

Therefore

Question 3: are the vertices of triangle .If is the mid-point of is the mid-point of , show that

Answer:

Ratio for being a midpoint:

Let the coordinates of the point

Therefore

Similarly

Let the coordinates of the point

Therefore

Question 4: is the mid-point of , find the co-ordinates of :

Answer:

i)

Therefore

ii)

Therefore

Question 5: is the midpoint of line segment as shown in the given figure. Find the co-ordinates of Points

Answer:

Therefore

Question 6: In the given figure, is mid-point of line segment .Find the co-ordinates of

Answer:

Therefore

Question 7: are the vertices of a triangle. Find the length of its median though the vertex

Answer:

.be the midpoint of .

Therefore

Question 8: Given a line in which . Find the co-ordinates of

Answer:

Question 9: One end of the diameter of a circle is Find the co-ordinates of the other end of it, if the center of the circle is

Answer:

be the other end of the diameter

Hence the coordinates of the other point of the diameter is

Question 10: are the vertices of quadrilateral .Find the co-ordinates of the midpoint of .Give a special name to the quadrilateral.

Answer:

be the midpoint of .

.be the midpoint of .

Because the diagonals bisect each other, the quadrilateral is a Parallelogram.

Question 11: are the vertices of parallelogram are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of

Answer:

Therefore

Therefore

Question 12: are the vertices of a parallelogram . Find the co-ordinates of vertex

Answer:

be the midpoint of

Therefore

Question 13: The points are midpoints of the sides of a triangle. Find its vertices.

Answer:

Let the vertices of the triangle be

Therefore

Therefore

Therefore

Adding i), iii) and v) we get

Adding ii), iv) and vi) we get

Using i), iii), v) and vii) we get

Similarly Using ii), iv), vi) and viii) we get

Hence the vertices are

Question 14: Points are collinear (i.e. lie on the same straight line) such that .Calculate the values of

Answer:

is the midpoint of .Therefore

Question 15: Points are collinear. If lies between , such that , calculate the values of

Answer:

is the midpoint of .Therefore

Question 16: Calculate the co-ordinates of the centroid of the triangle , if

Answer:

be the centroid of triangle .

Therefore

Hence the coordinates of the centroid are

Question 17: The co-ordinates of the centroid of a triangle are .lf ; calculate the co-ordinates of vertex

Answer:

be the centroid of triangle

Therefore

Hence the coordinates of P are

Question 18: are the vertices of the triangle whose centroid is the origin. Calculate the values of

Answer:

be the centroid of triangle

Therefore