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

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

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

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

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