Exercise 7.
2
Q1 : Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in
the ratio 2:3.
Answer :
Let P(x, y) be the required point. Using the section formula, we obtain
Therefore, the point is (1, 3).
Q2 : Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in
the ratio 2:3.
Answer :
Let P(x, y) be the required point. Using the section formula, we obtain
Therefore, the point is (1, 3).
Q3 : Find the coordinates of the points of trisection of the line segment joining (4, -
1) and (- 2, - 3).
Answer :
Let P (x1, y1) and Q (x2, y2) are the points of trisection of the line segment joining the given points i.e.,
AP = PQ = QB Therefore, point P divides AB internally in the ratio 1:2.
Point Q divides AB internally in the ratio 2:1.
Q4 : Find the coordinates of the points of trisection of the line segment joining (4,-1)
and (- 2, - 3).
Answer :
Let P (x1, y1) and Q (x2, y2) are the points of trisection of the line segment joining the given points i.e.,
AP = PQ = QB Therefore, point P divides AB internally in the ratio 1:2.
Point Q divides AB internally in the ratio 2:1.
Q5 : To conduct Sports Day activities, in your
rectangular shaped school ground ABCD, lines have
been drawn with chalk powder at a distance of 1 m
each. 100 flower pots have been placed at a distance
of 1 m from each other along AD, as shown in the
following figure. Niharika runs th the distance AD on
the 2nd line and posts a green flag. Preet runs th the
distance AD on the eighth line and posts a red flag.
What is the distance between both the flags? If Rashmi
has to post a blue flag exactly halfway between the line
segment joining the two flags, where should she post
her flag?
Answer :
It can be observed that Niharika posted the green flag at th of the distance i.e × 100 = 25 m
from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25).
Similarly, Preet posted red flag at th of the distance is × 100 = 20m from the starting point of 8th
line. Therefore, the coordinates of this point R are (8, 20).
Distance between these flags by using distance formula = GR
=
The point at which Rashmi should post her blue flag is the mid-point of the line joining these points.
Let this point be A (x,y).
Therefore, Rashmi should post her blue flag at 22.5m on 5th line.
Q7 : Find the ratio in which the line segment joining the points (- 3, 10) and (6, - 8) is
divided by (- 1, 6).
Answer :
Let the ratio in which the line segment joining ( - 3, 10) and (6, - 8) is divided by point ( - 1, 6) be k : 1.
Q8 : Find the ratio in which the line segment joining the points (- 3, 10) and (6, - 8) is
divided by (- 1, 6).
Answer :
Let the ratio in which the line segment joining ( - 3, 10) and (6, - 8) is divided by point ( - 1, 6) be k : 1.
Q9 : Find the ratio in which the line segment joining A (1, - 5) and B (- 4, 5) is divided
by the x-axis. Also find the coordinates of the point of division.
Answer :
Let the ratio in which the line segment joining A (1, - 5) and B ( - 4, 5) is divided by x-axisbe .
Therefore, the coordinates of the point of division is .
We know that y-coordinate of any point on x-axis is 0.
Therefore, x-axis divides it in the ratio 1:1.
Division point =
Q10 : Find the ratio in which the line segment joining A (1, - 5) and B (- 4, 5) is divided
by the x-axis. Also find the coordinates of the point of division.
Answer :
Let the ratio in which the line segment joining A (1, - 5) and B ( - 4, 5) is divided by x-axis bek:1.
Therefore, the coordinates of the point of division is .
We know that y-coordinate of any point on x-axis is 0.
Therefore, x-axis divides it in the ratio 1:1.
Division point =
Q11 : If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a
parallelogram taken in order, find x and y.
Answer :
Let (1, 2), (4, y), (x, 6), and (3, 5) are the coordinates of A, B, C, D
vertices of a parallelogram ABCD. Intersection point O of diagonal
AC and BD also divides these diagonals.
Therefore, O is the mid-point of AC and BD.
If O is the mid-point of AC, then the coordinates of O are
If O is the mid-point of BD, then the coordinates of O are
Since both the coordinates are of the same point O,
Q12 :If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a
parallelogram taken in order, find x and y.
Answer :
Let (1, 2), (4, y), (x, 6), and (3, 5) are the coordinates of A, B, C, D
vertices of a parallelogram ABCD. Intersection point O of diagonal AC
and BD also divides these diagonals.
Therefore, O is the mid-point of AC and BD.
If O is the mid-point of AC, then the coordinates of O are
If O is the mid-point of BD, then the coordinates of O are
Since both the coordinates are of the same point O,
Q13 : Find the coordinates of a point A, where AB is the diameter of circle whose
centre is (2, - 3) and B is (1, 4)
Answer :
Let the coordinates of point A be (x, y).
Mid-point of AB is (2, - 3), which is the center of the circle.
Q14 :Find the coordinates of a point A, where AB is the diameter of circle whose
centre is (2, - 3) and B is (1, 4)
Answer :
Let the coordinates of point A be (x, y).
Mid-point of AB is (2, - 3), which is the center of the circle.
Q15 : If A and B are ( - 2, - 2) and (2,-4),
respectively, find the coordinates of P
such that = and P lies on the
line segment AB.
Answer :
The coordinates of point A and B are ( - 2, - 2) and (2, - 4) respectively.
Since =
Therefore, AP: PB = 3:4
Point P divides the line segment AB in the ratio 3:4.
Q17 : Find the coordinates of the
points which divide the line segment
joining A (- 2, 2) and B (2, 8) into four
equal parts.
Answer :
From the figure, it can be observed that
points P, Q, R are dividing the line segment in
a ratio 1:3, 1:1, 3:1 respectively.
Q18 : Find the coordinates of the points which divide the line segment joining A(-2,2)
and B (2, 8) into four equal parts.
Answer :
From the figure, it can be observed that points P, Q, R
are dividing the line segment in a ratio 1:3, 1:1, 3:1
respectively.
Q19 : Find the area of a rhombus if its vertices are (3, 0),(4, 5), ( - 1, 4) and ( - 2, - 1)
taken in order. [Hint: Area of a rhombus = (product of its diagonals)]
Answer :
Let (3, 0), (4, 5), ( - 1, 4) and ( - 2, - 1) are the vertices A, B, C, D of a
rhombus ABCD.
Q20 : Find the area of a rhombus if its vertices are (3,0),(4, 5), (- 1, 4) and ( - 2, - 1)
taken in order. [Hint: Area of a rhombus = (product of its
diagonals)]
Answer : Let (3, 0), (4, 5), ( - 1, 4) and ( - 2, - 1) are the vertices A, B,
C, D of a rhombus ABCD.
