SECTION FORMULA WORKSHEET

Problem 1 :

Using the section formula, show that the points

A(1, 0),B (5, 3), C (2, 7) and D(-2, 4)

are vertices of a parallelogram taken in order.

Solution

Problem 2 :

The 4 vertices of a parallelogram are

A(-2, 3), B(3, -1), C(p, q) and D(-1, 9)

Find the value of  p and q.

Solution

Problem 3 :

Find the coordinates of the point which divides the line segment joining

(3, 4) and (-6, 2)

in the ratio 3:2 externally.

Solution

Problem 4 :

The coordinate of the midpoint of the line joining the point (2p, 4) and (-2, 2q) and (3, p). Find the value of q.

Solution

Problem 5 :

If the points P(a, -11), Q(5, b), R(2, 15) and S(1, 1) are the vertices of the parallelogram. Find the value of a and b.

Solution

Problem 6 :

In what ratio does the point (3, 12) divide the line segment joining the points (1, 4) and (4, 16).

Solution

Answer Key

1)  Two diagonals are intersecting at the same point. So the given vertex forms a parallelogram.

2)  p  =  4 and q  =  -1

3)   (-24 , -2)

4)  i)  q is 2

5)  So, the value of a and b is 4 and 3 respectively.

6)   2 : 1.

Problem 1 :

Find the coordinates of the point which divides the line segment joining (-3, 5) and (4, -9) in the ratio 1:6 internally.

Solution

Problem 2 :

Let A (-6 , -5) and B(-6 , 4) be the two points such that a point  P on the line AB satisfies AP = (2/9) AB. Find the point P.

Solution

Problem 3 :

Find the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4).

Solution

Problem 4 :

Find the ratio in which x axis divides the line segment joining the points (6, 4) and (1,- 7)

Solution

Problem 5 :

Find the coordinates of the point which divides the line segment joining the points A(4, -3) and B(9, 7) in the ratio 3 : 2.

Solution

Problem 6 :

Find the ratio in which the point P(-3, a) divides the join A(-5, 4) and B(-2, 3). Also find the value of a.

Solution

Problem 7 :

If the ratio in which the point P(a, 1) divides the join of A(-4, 4) and B(6, -1). Also find the value of a.

Solution

Asnwer Key

1)  (-2, 3) 

2)  So, P divides the line segment in the ratio 2:7 and the point is (-6, -3)

3)  Q divides the line segment in the ratio 2:1 and the required point is Q (-4, 2)

4)  So, x-axis divides the line segment in the ratio 4:7 and the point is Q (-4, 2)

5) So, the required point which is dividing the line segment in the ratio 3 : 2 is (7, 3).

6)  the value of a is 10/3.

7)   the required value of a is 2

Problem 1 :

Find the coordinates of the points of trisection of the line segment joining the points A(−5, 6) and B(4,−3).

Solution

Problem 2 :

The line segment joining A(6, 3) and B(−1, −4) is doubled in length by adding half of AB to each end. Find the coordinates of the new end points.

Solution

Problem 3 :

Find the coordinates of point of trisection of the segment joining points (4, -8) and (7, 4).

Solution

Problem 4 :

If A (5, -1), B (-3, -2) and C (-1, 8) are vertices of triangle ABC, find the length of median through A and find the coordinates of the centroid.

Solution

Problem 5 :

The line joining the points (2, 1) and (5, 8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0, find the value of k ?

Solution

Answer Key

1)  (-2, 3) and (1, 0)

2) C (5/2, -1/2),  D is (19/2, 13/2) and E is (-9/2, -15/2).

3)  the point A (5, -4), the point B is (6, 0).

4)  Centroid (1/3, 5/3), the length of median through A is √65.

5)  the value of k is -8/3.

Problem 1 :

Find the coordinates of the point which divides the line segment joining the points A(4,−3) and B(9, 7) in the ratio 3:2.

Solution

Problem 2 :

In what ratio does the point P(2,−5) divide the line segment joining A(−3, 5) and B(4, −9).

Solution

Problem 3 :

Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) in such a way that AP = (2/5) AB.

Solution

Problem 4 :

If the points A(4, 3) and B(x, 5) are on circle with center O(2, 3), then find the value of x.

Solution

Problem 5 :

Find the ratio in which the line 2x + 3y = 10 divide the line segment joining the points (1, 2) and (2, 3).

Solution

Problem 6 :

Determine the ration in which the point P(a, -2) divides the line joining of points A(-4, 3) and B(2, -4). Also find the value of a.

Solution

Problem 7 :

If the point C(-1, 2) divides internally the line segment joining A(2, 5) and in the ratio 3 : 4. Find the coordinate of B.

Solution

Answer Key

1)  (7, 3)

2)  the required ratio is 5 : 2 

3)  the required point is (3, 4).

4)  x = 2

5)  2 : 3.

6)  a = 2

7)  (-5, -2).

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