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Math Assignment Class X Ch-7 | Coordinate Geometry
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Math Assignment, Class X,
Questions based on distance formula
Find the distance between the following points:-
a) (-6, 7) and (-1, -5) Ans [13]
b) (a, 0) & (0, b) Ans [
c) (
d) (a + b, a - b) & (a - b, a + b) Ans [
Question 2
Find the distance of the following points from the origin:-
a) (5, -12) Ans [13]
b) (-5, 5) Ans [5
c) (-4, -6) Ans [2
Question 8
Find the
type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0)and C(-2, 5)
Ans [3, -3]
Ans [x = 6, -2, y = 8, 2]
Find p if A(6, 1), B(8, 2), C(9, 4), D(p, 3) are the vertices of a parallelogram
The mid- point of the line segment joining (2a , 4) & (-2, 3b) is (1, 2a + 1). Find the value of a & b.
In what ratio the line segment joining the points A(-2, -3) & (3, 7) is divided by the y-axis. Also find the coordinates of the point of division.
Ans [2 : 3, (0, 1)]
Find the ratio in which the line segment joining the points (-10, 2), & (3, -5) is divided by y-axis
In what
ratio the line segment joining the points (3, -5) and (-1, 6) divided by the
line y = x ?
Answer: 8:7
Question 23
Points A(-1,y) and B(5, 7) lie on a circle with centre O(2, -3y) such that AB is a diameter of the circle. Find the value of y. Also find the radius of the circle.
Answer: y = -1, Radius = 5
In what ratio does the line x - y - 2 = 0 divides the line segment joining (3, -1) & (8, 9) .
Question 27
Ans [5 : 2, a = 2/7]
Find the ratio in which the point (8/5, y) divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.
Answer: 3 : 2, y = 13/5
Question 29
Point P divides the line segment joining the points A(4, -5) and B(1, 2) in the ratio 5 : 2. Find the coordinates of point P.
Answer : (13/7, 0)
Question 30
Question 31
Ans [3, 1]
If A(2, 1), B(3, 4), C(0, 1) are three consecutive vertices of parallelogram. Find the 4th vertex.
Ans [-1, -2]
Find the length of the median of a triangle whose vertices are A(-1, 3), B(1, -1), C(5, 1)
Ans [5,
AD is a
median of triangle ABC with vertices A(5, -6), B(6, 4) and C(0,0). Find length
AD ?
P(-2, 5) and Q(3, 2) are two points. Find the coordinates of
the point R on line segment PQ such that PR = 2QR.
Answer: R(4/3, 3)
Question 37
Find a relation between x and y such that the points P(x, y) is equidistant from the points A(7, 1) and B(3, 5)
Answer: x - y - 2 = 0
Question 38
ABCD is a rectangle formed by the points A(-1, -1), B(-1,
6), C(3, 6) and D(3, -1). P, Q, R and S are mid-points of AB, BC, CD and DA
respectively. Show that diagonals of the quadrilateral PQRS bisect each other.
Solution Hint:
Find the coordinates of P,Q,R,S by using mid point formulas.
Find the coordinates of mid points of diagonals PR and QS which are same and are equal to (1, 5/2)
As the coordinates of mid points of PR and QS both are equal ⇒ Diagonals bisects each other.
Question 39Ans [-13, 7] [Hint:- point (-3, 1) is the mid -point of the point given point and the reflection]
Find the point on the y –axis which is equidistant from the points (5,-2) & (-3,2).
Questions based on the centroid of triangle
Find the centroid of the triangle whose vertices are given below
a) A(4,7), B(2,1), C(3,6) Ans [3, 14/3]
b) A(2,3), B(4,5), C(3,4) Ans [3,4]
Ans [56]
QUESTIONS DELETED FROM CBSE SYLLABUS
Ans [-3,21/13]
Prove that the points P(a, b+ c),Q(b, c+ a), R(c, a+ b) are collinear.
Question 4
Find a relation between x and y if the points (2,1),(x, y) and (7,5) are collinear.
(a) (3, 2), (4, k), (5, 3) Ans [5/2]
b) (3, 5), (m, 6), (1/2, 15/2) Ans [2]
c) (2, 5), (k, 11/2), (4, 6) Ans [3]
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