Question 1: Calculate the distance between the points correct to
decimal places.
Answer:
Question 2: Find the distance between the points correct to
significant figures.
Answer:
Question 3: Show that the points form an equilateral triangle.
Answer:
Therefore three sides are equal which makes it an equilateral triangle.
Question 4: The circle with center passes though the points
. Find the values of
Answer:
Distance of the points from the center are equal. Therefore
… … … … i)
… … … … ii)
Solving i) and ii), we get .
Therefore the center is
Question 5: The points are such that
. Find a linear relation between
Answer:
Question 6: Given a triangle in which
. A point
lies on
such that
. Find the length of line segment
Answer:
A point lies on
such that
.
Therefore
Length of
Question 7: are two fixed points. Find the co-ordinates of the point
in
such that:
. Also, find the co-ordinates of some other point
such that
Answer:
For P When Ratio:
Therefore
For Q When Ratio:
Therefore
Question 8: are the vertices of a triangle
. Point
lies on
lies on
such that
. Show that:
Answer:
When Ratio:
Therefore
When Ratio:
Therefore
Question 9: Find the coordinates of points of trisection of the line segment joining the point and the origin.
Answer:
Let be the two points dividing the points
and the origin in the ratio 1:2 \text{ and } 2:1 respectively.
Therefore
Therefore
Question 10: A line segment joining is divided in the ratio
, the point where the line segment
intersects the
(i) Calculate the value of
(ii) Calculate the co-ordinates of [1994]
Answer:
Therefore
Question 11: In what ratio is the line joining divided by the
? Write the co-ordinates of the point where
intersects the
[1993]
Answer:
Let the required ratio be and the point of
be
Question 12: The mid-point of the segment , as shown in diagram, is
. Write down the coordinates of
[1996]
Answer:
Therefore
Question 13: is a diameter of a circle with center
. If
, find
(i) the length of radius
(ii) the coordinates of [2013]
Answer:
Therefore
Question 14: Find the co-ordinates of the centroid of a triangle whose vertices are :
[2006]
Answer:
Let be the centroid of triangle
.
Therefore
Hence the coordinates of the centroid are
Question 15: The mid-point of the line segment joining . Find the values of
Answer:
Therefore
Question 16: The mid-point of the line segment joining . Find the values of
. [2007]
Answer:
Therefore
Question 17: (i) Write down the co-ordinates of the point that divides the line joining
in the ratio
.
(ii) Calculate the , where
is the origin.
(iii) In what ratio does the divide the line
? [1995]
Answer:
i) For P When Ratio:
Therefore
ii)
iii) Let the required ratio be and the point be
Question 18: Prove that the points are the vertices of an isosceles right-angled triangle. Find the co-ordinates of
so that
is a square. [1992]
Answer:
(two sides are equal). Hence triangle
is a isosceles triangle.
Question 19: is the mid-point of the line segment joining the points
. Find the coordinates of point
. Further, if
divides the line segment joining
and the origin in the ratio
, find the ratio
Answer:
For M When Ratio:
Therefore
Let divide MO in the ratio
Question 20: Calculate the ratio in which the line joining is divided by point
. Also, find (i)
(ii) length of
[2014]
Answer:
Let divide MO in the ratio