NCERT Class 10 Mathematics Co-Ordinate Geometry Formative Assessment CBSE Board Sample Problems

Get unlimited access to the best preparation resource for CBSE : fully solved questions with step-by-step explanation- practice your way to success.

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 2x + y - 4 = O 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