Skip to main content

CBSE TEST PAPER 10TH MATHEMATICS Distance and Section Formulae

1. Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1). 

 [Hint: let the point be P(x, y, z). given points be A(1, 2, 3) and B(3, 2, - 1). Then PA = PB] ans: x – 2z = 0

2.Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (– 4, 0, 0) is equal to 10. 

[Hint: let the point be P(x, y, z). given points be A(4, 0, 0) and B(-4, 0, 0). Then PA + PB = 10]

3.Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, – 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally. 

Ans: i) (-4/5, 1/5, 27/5) ii) (-8, 17, 3)

4.Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR. 

Ans : 1:2 

5. Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8). 

[hint: any point on YZ plane is of the form (0, y, z)] ans: 2:3 

6. Find the equation of the set of the points P such that its distances from the points A (3, 4, –5) and B (– 2, 1, 4) are equal. 

[hint: using distance formula PA and PB and equate it.] ans: 10 x + 6y – 18z – 29 = 0

7. Find the coordinates of the points which trisect the line segment joining the points P (4, 2, – 6) and Q (10, –16, 6). 

[hint: points of trisection divides the line segment into three equal parts. So use the ratio 1 : 2 and 2 : 1] 
Ans : (6, -4, -2) and (8, -10, 2)

8. The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, –5, 7) and (–1, 7, – 6), respectively, find the coordinates of the point C. 

[hint: use centroid formula. Let the third vertex be C(p, q, r)] 
ans: (1, 1, 2) 

9. Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex. 
Ans: (1, - 2, 8) 

10. If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then  find the values of a, b and c. 

[hint: use centroid formula] ans: a = - 2 , b = - 16/3, c = 2

Practice:

1.A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R. 
[hint: let coordinate of R = (4, y, z). let R divide PQ in the ratio k:1. Using section formula, find the coordinate of R and equate its x – coordinate to 4. Solve to find value of k. then using value of k , find y and z] 
ans: (4, -2, 6)

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'.

8. What point (or points) on the x-axis are at a distance of 5 units from the point (5, -4)?

9. Find point (or points) which are at a distance of 10 from the point (4, 3), given that the ordinate of the point (or points) is twice the abscissa.

10. Show that the points (3, 3), (9, 0) and (12, 21) are the vertices of a right angled triangle.

11. Show that the points (0, -1), (-2, 3), (6, 7) and (8, 3) are the vertices of a rectangle.

12. The points A(0, 3), B(-2, a) and C(-1, 4) are the vertices of a right angled triangle at A, find the value of a.

13. Show by distance formula that the points (-1, -1), (2, 3) and (8, 11) are collinear.

14. Calculate the co-ordinates of the point P that divides the line joining the points A (-1, 3) and B(5, -6)
internally in the ratio 1:2.

15. Find the co-ordinates of the points of trisection of the line segment joining the points (3, -3) and (6, 9).

16. The line segment joining A(-3, 1) and B(5, -4) is a diameter of a circle whose center is C. Find the co-
ordinates of the point C.

17. The mid-point of the line joining (a, 2) and (3, 6) is (2, b). Find the values of a and b.

18. The mid-point of the line segment joining (2a, 4) and (-2, 3b) is (1, 2a +1). Find the values of a and b.

19. The center of a circle is (1, -2) and one end of a diameter is (-3, 2), find the co-ordinates of the other end.

20. Find the reflection of the point (5, -3) in the point (-1, 3).


Answers



1. 3.61 units
2. 5units
3. 4 or -2
4. 74 units
5. A'(-2, 4), B'(-3, -2);
6. 1 units  6.24 units
7. (i) (-4, 3) (ii) (0, 5)
(iii) 2 5 units
8. (2, 0) and (8, 0 )
9. (1, 2), (3, 6)
10. 67.5 sq. units
12. 1  
14. (1, 0)
15. (4, 1), (5, 5)
16. (1,-3/2)
17. a = 1, b = 4
18. a = 2, b = 2
19. (5,-6)
20. (-7, 9)

 http://jsuniltutorial.weebly.com/  http://cbseadda.blogspot.com/
10th Maths SA-2 Chapter Quick links
Quadratic Equations
Circles
Co-ordinate Geometry
Arithmetic Progressions
Area Related to Circles
Probability
Height and Distance
Surface Areas and Volumes
Sample papers

Comments

  1. Let A(1, 2), B (4, 3) and C(6, 6).
    Let D (x, y) be the fourth vertex of the parallelogram ABCD.
    Midpoint of AC = [(1+6)/2 , (2+6)/2] = (7/2,4)
    Midpoint of BD = [(x+4)/2 , (y+3)/2
    Since, the diagonals of parallelogram bisect each other at O.
    ∴ Mid point of BD = Mid point of AC
    (7/2,4) = [(x+4)/2 , (y+3)/2
     7/2 = (x+4)/2
     x = 3
    also, 4 = (y+3)/2
    y = 8-3 =5

    Thus, (3, 5) is the fourth vertex.

    My jsuniltutorial offers CBSE Board course material free of cost Pls. use it and share to student

    ReplyDelete

Post a Comment

CBSE ADDA :By Jsunil Sir : Your Ultimate Destination for CBSE Exam Preparation and Academic Insights

Living science ratna sagar class 6 solutions

Ratna sagar living science 6 answers by jsunil. Class6 Living science solution Term-1 Living Science Solution chapter-1 Source of food Download File Living Science Solution chapter-2 Component of food Download File Living Science Solution chapter-3 Fibre to fabric Download File Living Science Sol ch-4 Sorting of material into group Download File Living Science Soln ch-5 Separation of substance Download File Living Science Solution chapter-6 Change around Us Download File Living Science Solution ch-7 Living and Non Living Download File Living Science Solution ch-8 Getting to Know Plants Download File Living Science Sol ch-9 The Body and Its movements Download File Visit given link for full answer Class6 Living science solution Term-II

Class 10 Chapter 02 Acid Bases and Salts NCERT Activity Explanation

NCERT Activity Chapter 02 Acid Bases and Salt Class 10 Chemistry Activity 2.1 Indicator Acid Base Red litmus No Change Blue Blue Litmus Red No change Phenolphthalein Colourless Pink Methyl Orange Pink   Yellow Indictors are substance which change colour in acidic or basic media. Activity 2.2 There are some substances whose odour changes in in acidic or basic media. These are called olfactory indicators. Like onion vanilla, onion and clove. These changes smell in basic solution. Activity 2.3 Take about 5 mL of dilute sulphuric acid in a test tube and add few pieces of zinc granules to it. => You will observe bubbles of hydrogen gas on the surface of zinc granules. Zn + H2SO4 --> ZnSO4 + H2 => Pass the Hydrogen gas through the soap solution. Bubbles formed in the soap solution as Hydrogen gas it does not get d...

Class 10 Metal and Non MetalsChapter 03 NCERT Activity Solutions

X Class 10 NCERT Activity Explanation Class 10 Metals and Non Metals Activity 3.1 Page No. 37 Take samples of iron, copper, aluminium and magnesium. Note the appearance of each sample. They have a shining surface. Clean the surface of each sample by rubbing them with sand paper and note their appearance again. They become more shiny. => Freshly cut Metal have shiny surface Activity 3.2 Page No. 37 Take small pieces of iron, copper, aluminium, and magnesium. Try to cut these metals with a sharp knife and note your observations. They are very hard to cut. Hold a piece of sodium metal with a pair of tongs and try to cut it with a knife. Sodium can be cut easily with knife. Hence K and Na are soft metal cut with knife Activity 3.3 Page No. 38 Take pieces of iron, zinc, lead and copper try to strike it four or five times with a hammer. These metals are beaten into thin sheet on hammering. This property of metal is called malleability and metals are called malleable. Activity 3.4 Page ...

Class 09 Atoms and Molecules Numerical Problem based on Law of chemical Combination(Solved)

Class 09 Atoms and Molecules Numerical Problem based on Law of chemical Combination Law of conservation of mass Law of constant proportion Empirical formula 1. If 10 grams of CaCO 3 on heating gave 4.4g of CO 2 and 5.6g of CaO, show that these observations are in agreement with the law of conservation of mass.(Based on Law of conservation of mass) Solution:  Mass of the reactants = 10g ;  Mass of the products = 4.4 + 6.6g = 10g Since the mass of the reactants is equal to the mass of the products, the observations are in agreement with the law of conservation of mass. 2. 1.375 g of cupric oxide was reduced by heating and the weight of copper that remained was 1.098g.  In another experiment 1.179 g of copper was dissolved in nitric acid and the resulting copper nitrate was converted into cupric oxide by ignition . The weight of cupric oxide formed was 1.476 g. which law of chemical combinations does this data state? Solution: in first experiment: Copper oxide = 1....

Structure of Matter class07

The language of chemistry class 7 Basic science soled questions. Q. What is chemistry? Ans: Chemistry is a branch of science in which we study the composition, structure, properties and change of matter. Q. What is matter? Ans: Anything that is around us having some mass and occupies space is called matter. Q. What are the different classifications of matter? Ans: Matters are classified into element, compound and mixture. Q. What is element? Ans: Elements are the purest form of substance (matter) made up of same kinds of particles. The smallest unit of element is an atom. eg. Hydrogen, oxygen, carbon. Q. What is compound?            See full post   The language of chemistry class 7 Basic science Class 07 Basic sciences Chapter the Language of Chemistry A. Answer these questions 1. What does the formula of a substance tell us? Answer: Formula of a compound or an element represents the name and number of atoms present ...