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NCERT Class 10 Mathematics Co-Ordinate Geometry Formative Assessment CBSE Board Sample Problems
Co-Ordinate Geometry Formative Assessment
Question 1
Calculate the Following
(a) Distance between the point and
Solution: D
(b) Mid-point of line segment AB where and
Solution: Mid-point is given by
(c) Area of the triangle formed by joining the line segments and
Solution: A
(d) Distance of point (5,0) from Origin
Solution:
(e) Distance of point (5, -5) from Origin
Solution:
(f) Coordinate of the point M which divided the line segment A (2,3) and B (5,6) in the ratio 2: 3
Solution: Coordinates of point M is given by
(g) Quadrant of the Mid-point of the line segment A (2,3) and B (5,6)
Solution: Midpoint is given by which lies in First quadrant
(h) The coordinates of a point A, where AB is the diameter of circle whose center is (2, -3) and B is (1,4)
Solution: We know that center is midpoint of AB, So
Solving these, we get (3, -10)
True or False Statement
Question 2
(a) Point and formed a quadrilateral
Solution: False, as three point are A, B and C are collinear, so no quadrilateral can be formed
(b) The point P lies on a circle of radius 6 and center
Solution: False, As the distance between the point P and C is which is less than 6. So point lies inside the circle
(c) Triangle PQR with vertices P and is similar to t XYZ with Vertices and
Solution: True. Both the triangle are equilateral triangle with side 4 and 8 respectively
(d) Point and are not collinear
Solution: True. As the Area formed by the triangle, XYZ is not zero
(e) The triangle formed by joining the point and is a right angle triangle
Solution: True, if we plot the point on the Coordinate system, it becomes clear that it is right angle at origin
(f) A circle has its center at the origin and a point A (5,0) lies on it. The point lies inside the circle
Solution: False. The radius of the circle is 5 and distance of the point B is more than 5, So it lies outside the circle
(g) The points and D in that order form a rectangle
Solution: True. If we calculate the distance between two points, it becomes clear that opposite side are equal, also the diagonal are equal. So it is a rectangle
Multiple-Choice Questions
Question 3
Find the centroid of the triangle XYZ whose vertices are and
(a)
(b)
(c)
(d)
Solution (d)
Centroid of the triangle is given by
Question 3
The area of the triangle ABC with coordinates as and
(a) -1
(b) 4
(c) 2
(d) 1
Solution (d)
Question 4
Find the value of p for which these points are collinear ?
(a) 2
(b) 4
(c) 3
(d) None of these
Solution a
For these points to be collinear
A = 0
Or
1
Question 5
Determine the ratio in which the line divides the line segment joining the points and
(a) 2: 9
(b) 1: 9
(c) 1: 2
(d) 2: 3
Solution (a)
Let the ratio be m: n
Now
Coordinate of the intersection
Now these points should lie of the line, So
Question 6
If the mid-point of the line segment joining the points A (3,4) and B (a, 4) is P (x, y) and x + y — 20 = 0, then find the value of a
(a) 0
(b) 1
(c) 40
(d) 45
Solution (d)
Mid-point
Now