Question 1: 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:
Question 2: 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 3: The mid-point of the segment , as shown in diagram, is
Write down the coordinates of
[1996]
Answer:
Therefore
Question 4: is a diameter of a circle with center
If
, find
(i) the length of radius
(ii) the coordinates of [2013]
Answer:
Therefore
Question 5: Find the co-ordinates of the centroid of a triangle whose vertices are :
[2006]
Answer:
Let be the centroid of triangle
Therefore
Question 6: The mid-point of the line segment joining Find the values of
[2007]
Answer:
Therefore
Question 7: (i) Write down the co-ordinates of the point that divides the line joining
in the ratio
(ii) Calculate the distance , where
is the origin.
(iii) In what ratio does the divide the line
? [1995]
Answer:
i) For P When Ratio:
Therefore
Therefore the point
ii)
iii) Let the required ratio be and the point be
Question 8: 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 9: 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
Question 10: Calculate the ratio in which the line joining is divided by the line
[2006]
Answer:
Let the required ratio be and the point of
be
Now calculate the coordinate of the point of intersection
Co-ordinates of the point of intersection =
Question 11: lf
(i) find the length of
(ii) In what ratio is the line joining , divided by the
? [2008]
Answer:
Let the required ratio be and the point of
be
Question 12: The line segment joining is intercepted by
at the point
Write down the ordinate of the point
Hence, find the ratio in which
divides
Also, find the co-ordinates of the point
[1990, 2006]
Answer:
Let the required ratio be and the point of
be
Question 13: In the given figure, line meets the
at point
at point
is the point
Find the co-ordinates of
[1999, 2013]
Answer:
Therefore
Question 14: Given a line segment joining the points
Find:
i) The ratio in which is divided by
ii) Find the coordinates of point of intersection
iii) The length of [2012]
Answer:
Let the required ratio be and the point of intersection
be
Length of
Question 15: is a straight line of
units. If
has the coordinates
has the coordinates
, find the value of
[2004]
Answer:
are the two points.
Distance between them is units.
Therefore
Question 16: The mid point of the line segment joining (3m, 6) and (-4, 3n) is (1, 2m-1). Find the values of m and n. [2006]
Answer:
Therefore
Question 17: is a triangle and
is the centroid of the triangle. If
, find
Find the length of the side
[2011]
Answer:
is the centroid
units.