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:
Therefore for
Hence
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
Since
Therefore
Therefore
Question 3: The mid-point of the segment , as shown in diagram, is
. Write down the coordinates of
. [1996]
Answer:
Given Midpoint of
Therefore
Therefore
Question 4: is a diameter of a circle with center
. If
, find
(i) the length of radius
(ii) the coordinates of . [2013]
Answer:
Given Midpoint of
Therefore
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
Hence the coordinates of the centroid are
Question 6: The mid-point of the line segment joining . Find the values of
. [2007]
Answer:
Given Midpoint of
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
Since
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:
Since (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
Since
Since
Question 10: Calculate the ratio in which the line joining and
is divided by the line
. [2006]
Answer:
Let the required ratio be and the point of
be
Since
Now calculate the coordinate of the point of intersection
Co-ordinates of the point of intersection =
Question 11: lf and
(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
Since
Question 12: The line segment joining and
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
Since
Therefore the point
Question 13: In the given figure, line meets the
at point
and
at point
.
is the point
and
Find the co-ordinates of
. [1999, 2013]
Answer:
Given
Therefore
Therefore .
Question 14: Given a line segment joining the points
and
. 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
Since
Therefore the point intersection is
Length of .
Question 15: is a straight line of
units. If
has the coordinates
and
has the coordinates
, find the value of
. [2004]
Answer:
and
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:
Given Midpoint of
Therefore
Question 17: is a triangle and
is the centroid of the triangle. If
, find
. Find the length of the side
. [2011]
Answer:
Since is the centroid
Therefore
Therefore units.