NCERT Class 10 Mathematics Co-Ordinate Geometry Formative Assessment CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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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

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