Assignment-Coordinate Geometry

1.If the vertices of a triangle are (2,4), (5,k) and (3,10) and its area is
15 sq cm. Find the value of k.
2. Find the distance of a point (2,3) from origin.
3. The three vertices of a rhombus, taken in order are (2,-1), (3,4) and
(-2,3). Find the fourth vertex.
4. Are (4,8) ,(7,5) and (1,-1) the vertices of a right triangle?
5. There are two points A(-2,-3) and B(2,3). Is the distance of these
points from origin is same?
6. If (-2,-1), (a,0), (4,3) and (1,2) are the vertices of a parallelogram.
Find the value of a.
7. Find the distance between the points (-4,p) and (5,q).
8. Find the area of the triangle formed by the points P(2,1), Q(6,1) and
R(2,4).
9. On which axis the point (-5,0) lie?
10. Find the value of p for which the points (-1,3) , (2,p) and (5,-1) are
collinear.
11. Find the relation between x and y if the points (x,y),(1,2) and (7,0) are
collinear.
12. Find the coordinates of the point which divides the line segment
joining the points (4, – 3) and (8, 5) in the ratio 3 : 1 internally.
13. If A(–5, 7), B(– 4, –5), C(–1, –6) and D(4, 5) are the vertices of a
quadrilateral, find the area of the quadrilateral ABCD.
14. Find a relation between x and y such that the point (x , y) is
equidistant from the points (7, 1) and (3, 5).
15. Find the coordinates of the points of trisection of the line segment
joining the points A(2, – 2) and B(– 7, 4).
16. If A(5, -1), B(-3, -2) and C(-1, 8) are the vertices of triangle ABC, find
the length of median through A and the coordinates of the centroid.
17. Prove that the points (-3, 0), (1, -3) and (4,1) are the vertices of an
isosceles right angled triangle. Find the area of this triangle.
18. Find the area of the triangle formed by joining the mid – points of the
sides of the triangle whose vertices are (0, -1),(2, 1) and (0, 3).
Find the ratio of the area of the triangle formed to the area of the given
triangle.
19. If A( -2, -1) , B( a, 0) C( 4, b) and D(1, 2) are the vertices of a
parallelogram , find the values of a and b.
20. Let the opposite points of a square be ( 3, 4) and (1, -1) . Find the
coordinates of the remaining angular points.
21. If two vertices of an equilateral triangle be ( 0 , 0) , ( 3 , √3 ). Find the
third vertex.
22. If the point C ( -1 ,2) divides internally the line segment joining A(2,5)
and B in the ratio 3:4. Find the coordinates of B.
23. Find the coordinates of the circumcentre of the triangle whose
vertices are (8,6) (8,-2) and (2,-2) .
24. If the vertex of a triangle be (1,1) and the middle points of the sides
through it be ( -2 , 3) and (5,2). Find the other vertices.
25. In the figure BOA is a right triangle and C is the midpoint of hypt
AB.Show that it is equidistant from the vertices O,A and B.