CBSE: 10th Class Sample Test Paper - Coordinate Geometry

CBSE: 10th Class Sample Test Paper - Coordinate Geometry

Q.1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).
Q.2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the ratio 3: 4.
Q.3. Show that the points (1, 1), (3, -2) and (-1, 4) are collinear.
Q.4. Find the centroid of the triangle whose vertices are (3, -5); (- 7, 4) and (10, - 2).
Q.5. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7)
Q.6. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.
Q.7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

Q.8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.
Q.9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x1, y1), B(x2, y2) and C(x3, y3) are given by (x1+x2+x3)/3  , (y1+y2+y3)/3
Q.10. Prove that the diagonals of a rectangle bisect each other and are of equal length.
Q.11. Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1.
Q.12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).
Q.13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis respectively, find the coordinates of the vertices of the square PQRS.
Q.14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that x2 + y2 - 8x - 10y + 39 = 0
Q.15. The line segment joining the points (3, - 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, - 2) and (5/3, q) respectively, Find the value of p and q.

Q.16. Find the points on the y axis whose distances from the points (6, 7) and (4,-3) are in the ratio 1:2

Q.17 Determine the ratio in which the line 2x + y -4 = 0 divide the line segment joining the points A (2,-2) and B (3, 7).Also find the coordinates of the point of division

Q.18. Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3).

Q.19. If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and its area is 15 sq units, find the value (s) of k..
   
Q.20.The centre of a circle is (2x – 1, 3x + 1).Find x if the circle passes through (-3,-1) and the length of the diameter is 20 units Q.21. If A & B are (-2,-2) and (2,-4) respectively, find the co ordinates of P such that    AP = AB and P lies on the line segment AB.

Q.22. Show that the points (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order are the vertices of a rhombus. Also find the area of the rhombus.

Q.23. If A, B and P are the points (-4, 3), (0, -2) and (ab) respectively and P is equidistant from A and B, show that 8a - 10b + 21= 0

Q.24If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex

Q.25. Find the centre of a circle passing through the points (6, -6), (3, -7) and (3, 3).Also find the radius.. .