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.
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.
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.
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.
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.
Problem 6 :
In what ratio does the point (3, 12) divide the line segment joining the points (1, 4) and (4, 16).
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.
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.
Problem 3 :
Find the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4).
Problem 4 :
Find the ratio in which x axis divides the line segment joining the points (6, 4) and (1,- 7)
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.
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.
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.
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).
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.
Problem 3 :
Find the coordinates of point of trisection of the segment joining points (4, -8) and (7, 4).
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.
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 ?
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.
Problem 2 :
In what ratio does the point P(2,−5) divide the line segment joining A(−3, 5) and B(4, −9).
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.
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.
Problem 5 :
Find the ratio in which the line 2x + 3y = 10 divide the line segment joining the points (1, 2) and (2, 3).
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.
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.
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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