### Common Errors in Secondary Mathematics

Common Errors Committed  by the  Students  in Secondary Mathematics   Errors  that students often make in doing secondary mathematics  during their practice and during the examinations  and their remedial measures are well explained here stp by step.  Some Common Errors in Mathematics

### Math Assignment Class X Ch-7 | Coordinate Geometry

Math Assignment, Class X,

Chapter 7 Coordinate Geometry

Extra questions of chapter 7 class 10 Coordinate Geometry with answer and  hints to the difficult questions. Important and useful math assignment for the students of class 10

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 STANDARDCOORDINATE GEOMETRY

Question 1
Find the distance between the following points:-
a) (-6, 7) and (-1, -5) Ans 

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 

b) (-5, 5)       Ans [5 ]

c) (-4, -6)     Ans 

Question 3
Find the coordinates of the point equidistant from the points A(-2,-3), B(-1,0), C(7,-6)
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
Ans [3:5, b = 5/2,]

Question 5
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]

Question 7
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)
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
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 [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.
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) .
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.

Question 17
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
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
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.
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.
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
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
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]

Question 32

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).
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
Ans [(4, 3), (6, 5), (4, 9)]

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 40
Find 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 
c) (2, 5), (k, 11/2), (4, 6)        Ans 

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