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Math Assignment Class X Ch-7 | Coordinate Geometry
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Math Assignment, Class X,
Chapter 7 Coordinate Geometry
For better results
- Students should learn all the basic points of Coordinate Geometry
- Student should revise N C E R T book thoroughly with examples.
- Now revise this assignment. This assignment integrate the knowledge of the students.
ASSIGNMENT FOR 10 STANDARD
COORDINATE GEOMETRY
Question 1Find the distance between the following points:-
a) (-6, 7) and (-1, -5) Ans [13]
b) (a, 0) & (0, b) Ans []
c) (+1, 1) & (0, ) Ans []
d) (a + b, a - b) & (a - b, a + b) Ans [b]
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]
Find the coordinates of the point equidistant from the points A(-2,-3), B(-1,0), C(7,-6)
Ans [3,-3]
Ans [3,-3]
Question 4
Find the ratio in which the point P(b, 1) divides the join of A(7, -2) and B(-5, 6). Also find b
Find the ratio in which the point P(b, 1) divides the join of A(7, -2) and B(-5, 6). Also find b
Ans [3:5, b = 5/2,]
Find the ratio in which the point P(a, -2) divides the join of A(-4, 3), & B(2, -4). Also find a.
Ans [5 : 2, a = 2/7]
Question 6
The coordinates of the mid- point of the line joining the points (2p + 2, 3) & (4, 2q + 1) is (2p, 3q). Find the value of p & q.
Ans [3, 1]
The coordinates of the mid- point of the line joining the points (2p + 2, 3) & (4, 2q + 1) is (2p, 3q). Find the value of p & q.
Ans [3, 1]
If A (6,-1), B(1,3), C (k,8) are such that AB = BC. Then find the value of k
Ans [k = 5, -3]
Question 8
Find the coordinates of the point equidistant from the A(5, 8), B(5, -5),and C (1, -5)
Find the coordinates of the point equidistant from the A(5, 8), B(5, -5),and C (1, -5)
Ans [3, 3/2]
Question 9
Find the type of quadrilateral formed by:-
a) A(2, -2), B(14, 10), C(11, 13), D(-1, 1) Ans
[Rectangle]
b) A(0,-2), B(3,1), C(0,4), D(-3,1) Ans [Square]
c) A(-3,5), B(3,1), C(0,3), D(-1,-4) Ans [No]
d) A(4,5), B(7,6), C(4,3), D(1,2) Ans
[Parallelogram]
e) A(3,0), B(4,5), C(-1,4), D(-2,-1) Ans [Rhombus]
Question 10
Question 13
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.
Question 19
Question 31
Question 32
Question 34
Prove that the points P(a, b+ c),Q(b, c+ a), R(c, a+ b) are collinear.
Question 35
Find a relation between x and y if the points (2,1),(x, y) and (7,5) are collinear.
In what ratio the line segment joining the points (-2, -3) & (3, 7) divided by the y-axis. Also find the coordinates of the point of division.
Ans [2:3, (0, 1)]
Question 11
Find p if A(6, 1), B(8, 2), C(9, 4), D(p, 3) are the vertices of a parallelogram
Ans [2:3, (0, 1)]
Question 11
Find p if A(6, 1), B(8, 2), C(9, 4), D(p, 3) are the vertices of a parallelogram
Ans [p = 7]
Question 12
The mid- point of the line segment joining (2a+4) & (-2,3b) is (1,2a+1). Find the value of a & b.
The mid- point of the line segment joining (2a+4) & (-2,3b) is (1,2a+1). Find the value of a & b.
Ans [a = b = 2]
Question 13
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, point of division (0,1)]
Question 14
The centre of the circle is (2a-1, 7) and is passes through the point (-3, -1). If the diameter of the circle is 20cm. Find the value of a.
Ans [a = -4, 2]
Question 15
In what ratio does the line x - y - 2 = 0 divides the line segment joining (3, -1) & (8, 9) .
In what ratio does the line x - y - 2 = 0 divides the line segment joining (3, -1) & (8, 9) .
Ans [2 : 3]
Question 16
Prove that the points A(0, 0), B(5, 5), C(-5, 5)are the vertices of a right isosceles triangle.
Prove that the points A(0, 0), B(5, 5), C(-5, 5)are the vertices of a right isosceles triangle.
Question 17
Find the centre of the circle passing through the points (6, -6), (3, -7) & (3, 3)
Find the centre of the circle passing through the points (6, -6), (3, -7) & (3, 3)
Question 18
The points A(2, 9), B(a, 5), C(5, 5)are the vertices of a right angled triangle at B. Find a and the area of triangle ABC
Ans [a = 2, Area = 6cm2]
Question 19
Show that the point p(-4, 2) lies on the line segment joining the points A(-4,6) & B(-4,-6)
Question 20
If A(2,1), B(3,4), C(0,1) are three consecutive vertices of parallelogram. Find the 4th vertex.
Ans [-1,-2]
Question 21
If A(2,1), B(3,4), C(0,1) are three consecutive vertices of parallelogram. Find the 4th vertex.
Ans [-1,-2]
Question 21
Find the value of k if P(2,4) is equidistant from the points A(5, k) & B(k,7)
Ans [k = 3]
Question 22
Find the length of the median of a triangle whose vertices are A(-1, 3), B(1, -1), C(5, 1)
Ans [5, , 5]
Question 23
Find the ratio in which the line segment joining the points (-10,2), & (3,-5) is divided by y-axis
Find the length of the median of a triangle whose vertices are A(-1, 3), B(1, -1), C(5, 1)
Ans [5, , 5]
Question 23
Find the ratio in which the line segment joining the points (-10,2), & (3,-5) is divided by y-axis
Ans [10:3]
Question 24
If (-2,2), (x,8) & (6,y) are three concyclic points whose centre is (2,5). Find x and y.
Ans [x = 6,-2, y = 8, 2]
Question 25
The opposite vertices of a square are (-1, 2), (3, 2). Find the coordinates of other two vertices.
Question 24
If (-2,2), (x,8) & (6,y) are three concyclic points whose centre is (2,5). Find x and y.
Ans [x = 6,-2, y = 8, 2]
Question 25
The opposite vertices of a square are (-1, 2), (3, 2). Find the coordinates of other two vertices.
Ans [(1,4),(1,0)]
Question 26
If the line joining the points (2, 1) & (5, -8) is trisected by the points P & Q. If point P lie on the line 2x - y + k = 0 Find k.
Question 26
If the line joining the points (2, 1) & (5, -8) is trisected by the points P & Q. If point P lie on the line 2x - y + k = 0 Find k.
Ans [k = -8]
Question 27
Find the reflection (image) of the point (7,-5) in the point (-3,1)
Ans [-13,7] [Hint:- point (-3,1) is the mid -point of the point given point and the reflection]
Question 28
Find the ratio in which the point (-3, k)divides the line segment joining the points (-5, -4) & (-2, 3). Hence find the value of k
Question 27
Find the reflection (image) of the point (7,-5) in the point (-3,1)
Ans [-13,7] [Hint:- point (-3,1) is the mid -point of the point given point and the reflection]
Question 28
Find the ratio in which the point (-3, k)divides the line segment joining the points (-5, -4) & (-2, 3). Hence find the value of k
Ans [2:1, k = 2/3]
QUESTIONS DELETED FROM CBSE SYLLABUS
Question 29
If A(1, k), B(4, -3), C(-9, 7)are the vertices of triangle and its area is 15 sq. Unit. Find k
Ans [-3,21/13]
Question 30
Ans [-3,21/13]
Question 30
If the coordinates of the mid –points of the sides of a triangle are (1,1), (2,-3), and (3,4).Find the coordinates of the centroid of the triangle.
Ans 2, 2/3
Question 31
Coordinates of the mid points of sides of a triangle are A(1,1), B(2,-3), C(3,4). Find the centroid of the triangle ABC.
Ans [2,2/3]
Find the centroid of the following points:-
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]
Question 33
Find the value of p for which A(-5, 1), B(1, p), C(4, -2) are collinear
Ans [p = -1]
Question 34
Prove that the points P(a, b+ c),Q(b, c+ a), R(c, a+ b) are collinear.
Question 35
Find a relation between x and y if the points (2,1),(x, y) and (7,5) are collinear.
Ans [4x - 5y = 3]
Question 36
Find the point on the y –axis which is equidistant from the points (5,-2) & (-3,2).
Question 36
Find the point on the y –axis which is equidistant from the points (5,-2) & (-3,2).
Ans [(0,-2)]
Question 37
If the points A(x, y), B(-5, 7) and C(-4, 5) are collinear then show that 2x + y + 3 = 0
Question 38
The mid point of the sides of a triangle are (5,4),(4,6) and (5,7).Find the coordinates of the vertices of the triangle
The mid point of the sides of a triangle are (5,4),(4,6) and (5,7).Find the coordinates of the vertices of the triangle
Ans [(4, 3), (6, 5), (4, 9)]
Question 39
Question 39
If A(5, -1), B(-3, -2), C(-1, 8)are the vertices of triangle ABC. Find the length of the median through A and the centroid of the triangle .
Ans [] , (1/3, 5/3)
Question 40Find the value of k for which the following points 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]
(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]
Question 41
Two vertices of a triangle ABC are given by A(6,4) & B(-2,2) and its centroid is (3,4). Find the coordinates of the third vertex C of triangle ABC.
Ans [56]
Ans [56]
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