Note: We will use the formula. If a point divides two points , then the coordinates of the point at
Question 1: Calculate the co-ordinates of the point which divides the line segment joining:
Answer:
Let the coordinates of the point
Therefore
Let the coordinates of the point
Therefore
Question 2: In what ratio is the line joining divided by the
Answer:
Let the required ratio be and the point of
be
Question 3: In what ratio is the line joining divided by the
Answer:
Let the required ratio be and the point of
be
Question 4: In what ratio does the point divide the join of
? Also, find the value of
Answer:
Let the point divide the join of
Now calculate
Question 5: In what ratio does the point divide the join of
? Also, find the value of
Answer:
Let the point divide the join of
Now calculate
Question 6: In what ratio is the join of divided by the
. Also, find the co-ordinates of the point of intersection.
Answer:
Let the required ratio be and the point of
be
Now calculate the coordinate of the point of intersection
Question 7: Find the ratio in which the join of is divided by the
. Also, find the co-ordinates of the point of intersection.
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 8: Points divide the line segment joining the point
and the origin in five equal parts. Find the co-ordinates of
Answer:
For
Ratio
Hence the coordinates of
For
Ratio
Hence the coordinates of
Question 9: The line joining the points is divided by the point
such that
Find the co-ordinates of
Answer:
This implies that
Hence the coordinates of the point
Question 10: is a point on the line joining
such that
Find the coordinates of
Answer:
This implies that
Question 11: Calculate the ratio in which the line joining the points is divided by the line
. Also, find the co-ordinates of the point of intersection.
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 12: 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 13: The point divides the line segment
, as shown in the figure, in the ratio
. Find the co-ordinates of points
.
Answer:
Therefore
Question 14: Find the co-ordinates of the points of trisection of the line joining the points
Answer:
When
Therefore
When
Therefore
Question 15: Show that the Line segment joining the points is trisection by the co-ordinate axes.
Answer:
Let the two points trisecting the points are
.
When Ratio for B:
Therefore
When Ratio for A:
Therefore
Question 16: Show that is a point of trisection of the line-segment joining the points
. Also find the co-ordinates of the other point of trisection.
Answer:
Let the point divide the join of
For the other point
When
Therefore
Question 17: 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 18: The line segment joining the points is intersected by the
at point
. Write down the abscissa of
. Hence, find the ratio in which
divides
. Also, find the co-ordinates of
.
Answer:
Let the required ratio be and the point of
be
Question 19: are the co-ordinates of the vertices of the triangle
. Points
lie on
respectively, such that:
.
\displaystyle \text{(ii) Show that
Answer:
Therefore
Therefore
Question 20: are the vertices of a triangle
. Find the length of line segment
, where point
lies inside
, such that
Answer:
For P When
Therefore
Question 21: 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 22: The line segment joining is intercepted by the
at the point
. Write down the abscissa of the point
. Hence, find the ratio in which
divides
. Also, find the co-ordinates of the point
Answer:
Let the required ratio be and the point of
be
Question 23: The line joining intersects the
at point
.
are perpendiculars from
on the
. Find:
Answer:
Let the required ratio be and the point of
be
sq. units
Question 24: In the given figure, line meets the
at point
at point
.
is the point
Find the co-ordinates of
. [1999, 2013]
Answer:
Therefore
.
Question 25: 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
Therefore the point intersection is
Length of .