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