X Maths Co-Ordinates geometry Formula

10th maths Test paper Co-Ordinate Geometry

1. Calculate the distance between the points P(2, 2), Q(5, 4) correct to three significant figures. (Do not consult tables).

2. A is a point on the y-axis whose ordinate is 5 and B is the point (-3, 1). Calculate the length of AB.

3. The distance between A(1, 3) and B(x, 7) is 5. Find the possible values of x.

4. P and Q have co-ordinates (-1, 2) and (6, 3) respectively. Reflect P in the x-axis to P'. Find the length

of the segment P'Q.

5. Point A(2, -4) is reflected in the origin as A'. Point B(-3, 2) is reflected in x-axis at B'. Write the co-ordinates of A' and B'. Calculate the distance A'B' correct to one decimal place.

6. The center of a circle of radius 13 units is the point (3, 6). P(7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.

7. A and B have co-ordinates (4, 3) and (0, 1) respectively. Find (i) the image A' of A under reflection in the y-axis.

(ii) the image B' of B under reflection in the line AA'.

(iii) the length of A'B'.

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CBSE ADDA: CBSE TEST PAPER 10TH MATHEMATICS ...

Assignments class 10 Chapter Co-Ordinate

Q1. Find the distance between the following points:

(a) A(3 , 5) and B(8 , – 7) (b)P( a + b , a – b ) and Q ( a– b , –a – b )

Q2. Find the value of x for which the distance between points A(x, 7) and B (–2, 3) is 4√5 units.

Q3. If the points (3, 2) and (2, –3) are equidistant from points (x, y) show that x + 5y = 0.

Q4. Show that the following points are collinear:
(a) (–5, 6), (–1, 2) and (2, –1)
(b) (4, 3) , (5,1 ) and (1, 9)

Q5. Show that following points are vertices of right triangle. Also, name the right angle.
(a)(4, 4) , ( 3 , 5) , (–1 ,1)
(b)(–2, 3) , ( 8, 3) , ( 6, 7)

Q6. Show that following points are vertices of a rectangle:
(a) (2 , –2) , ( 8, 4) , ( 5, 7 ) , (– 1, 1)
b)(–4 , –1) , (–2 , 4) , ( 4, 0 ) , ( 2, 3 )

Q7. Show that following points are vertices of a square:
a) ( 0 , –1) , ( 2, 1) , ( 0, 3) , (–2, 1)
(b)( 0, 1) , ( 1, 4) , ( 4,3) , ( 3, 0)

Q8. Show that following points are vertices of rhombus:

(a) ( 0, 5 ) , (–2, –2 ) , ( 5 , 0 ) , ( 7, 7 ) (b ) ( 2, –1) , ( 3, 4) , (–-2, 3) , (–3 , –2)

Q9. Show that the points ( a, a ) , (–a, –a ) and (–√3 a , √3 a) form an equilateral triangle.

Q10. Find the co-ordinates of circumcenter of a ∆ ABC where A( 1, 2) ,B ( 3, –4) and C ( 5, –6 ).

Q11. Find radius of the circle, the co-ordinates of the ends of whose diameter are (–1, 2) and (3, –4 ).

Q12. (a) Find the point on x-axis, which is equidistant from points ( 7, 6 ) and ( 9 , 4 ).

(b)Find the point on y-axis, which is equidistant from points ( 5, 2 ) and (–4 , 3 ).

Q13. A point P is at a distance of√10 from the point ( 4, 3). Find the co-ordinates of P, if its ordinate is twice its abscissa.

Q14. A line of length 10 units has (–-2, 3) as one of its end points. If the ordinate of the other end be 9, Show that its abscissa is 6 or–10.

Q15. The opposite angular points of a square be ( 3, 4 ) and ( 1, –1). Find the co-ordinates of the remaining angular points.

Answers

Ans 1 . (a) 13, (b) 2 √a² + b²

Ans 2. 6 or – 10

Ans 10. (11, 2)

Ans11.√13

Ans12. (a) (3, 0)(b ) (0, 15)

Ans13. (3, 6)

Ans15. (9/2, 1/2) and (–1/2 , 5/2 )

CBSE TEST PAPER Chap-4(co-ordinate geometry)

Choose the correct answer from the given four options:

1. The distance of the point P (2, 3) from the x-axis is

(A) 2       (B) 3         (C) 1                           (D) 5

2. The distance between the points A (0, 6) and B (0, –2) is

(A) 6                            (B) 8                (C) 4                           (D) 2

3. The distance of the point P (–6, 8) from the origin is

(A) 8                            (B) 2 √7          (C) 10                         (D) 6

4. The distance between the points (0, 5) and (–5, 0) is

(A) 5                           (B) 5√ 2          (C) 2 √5                      (D) 10

5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5                            (B) 3                (C) √ 34                   (D) 4  

Section-B

1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).

2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the 
ratio 3: 4.

3. Show that the points (1, 1), (3, - 2) and (- 1, 4) are collinear.

4. Find the centroid of the triangle whose vertices are (3, - 5); (- 7, 4) and (10, - 2).

5. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.

6. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7) is equal, show that 3x = 2y.

7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.

9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are given by  [(x₁+x₂+x₃)/3] , [ )y₁+y₂+y₃)/3]

10. Prove that the diagonals of a rectangle bisect each other and are of equal length

11. Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1.

12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).

13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis respectively, find the coordinates of the vertices of the square PQRS.

14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that   x² + y² - 8x -10y + 39 = 0

15. The line segment joining the points (3, - 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, Find the value of p and q.

10th Maths SA-2 Chapter Links

Quadratic Equations

Arithmetic Progressions

Height and Distance

Co-ordinate Geometry

Circles

Area Related to Circles

Surface Areas and Volumes

Probability

10th Section formula