OP Malhotra Coordinate Geometry Class-10 S.Chand ICSE Maths Solutions Ch-11

OP Malhotra Coordinate Geometry Class-10 S.Chand ICSE Maths Solutions Ch-11.  We Provide Step by Step Answer of Exe-11 with Self Evaluation and Revision of S Chand OP Malhotra Maths . Visit official Website CISCE  for detail information about ICSE Board Class-10.

OP Malhotra Coordinate Geometry Class-10 S.Chand ICSE Maths Solutions Ch-11

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-: Select Topics :-

Exercise-11(a)

Exercise-11(b)

Exercise-11(c)

Self Evaluation And Revision

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Exercise-11

OP Malhotra Coordinate Geometry Class-10 S.Chand ICSE Maths Solutions Ch-11

Coordinate Geometry:

• Position of a point P in the Cartesian plane with respect to co-ordinate axes is represented by the ordered pair (x, y).
  
• The line X’OX is called the X-axis and YOY’ is called the Y-axis.
• The part of intersection of the X-axis and Y-axis is called the origin O and the co-ordinates of O are (0, 0).
• The perpendicular distance of a point P from the Y-axis is the ‘x’ co-ordinate and is called the abscissa.
• The perpendicular distance of a point P from the X-axis is the ‘y’ co-ordinate and is called the ordinate.
• Signs of abscissa and ordinate in different quadrants are as given in the diagram:
  
• Any point on the X-axis is of the form (x, 0).
• Any point on the Y-axis is of the form (0, y).

Section formula. The coordinates of the point which divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m : n are:

The above formula is section formula. The ratio m: n can also be written as 𝑚𝑛 : 1 or k : 1, The
co-ordinates of P can also be written as P(x,y) = 𝑘𝑥2+𝑥1𝑘+1,𝑘𝑦2+𝑦1𝑘+1

The mid-point of the line segment joining the points P(x1, y1) and Q(x2, y2) is

Here m : n = 1 :1.

Area of a Triangle. The area of a triangle formed by points A(x1 y1), B(x2, y2) and C(x3, y3) is given by | ∆ |,
where ∆ =½[𝑥1(𝑦2−𝑦3)+𝑥2(𝑦3−𝑦1)+𝑥3(𝑦1−𝑦2)]
where ∆ represents the absolute value.

Area of a quadrilateral, ABCD = ar(∆ABC) + ar(∆ADC)

How to Solve the  line segment bisection ,trisection and four-section problem’s:

1. You will be given coordinates of the two point A , B
2. If the problem is to find bisection, then you can simply found the mid point using
3. If the problem is to find trisection(three equal parts of the line ).Let us assume the point are P and Q, then AP=PQ=QB
   Now P divides the line AB into 1:2 part
   While Q divides the line AB into 2:1 part
   So we can use section formula to get the coordinate of point P and Q
4. If the problem is to find four equal parts .Let us assume the point are P ,Q And R  such that AP=PQ=QR=RB
   Now P divides the line AB into 1:3 part
   Q divides the line AB into 1:1 part
   R divides the line AB into 3:1 part
   So we can use section formula to get the coordinate of point P  ,Q and R

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Exe-11(a),

OP Malhotra Coordinate Geometry Class-10 S.Chand ICSE Maths Solutions Ch-11

Question 1:

Find the mid point of lines joining

(a) (5, 8), (9, 11)

(b)…………………

Question 2:

Find the mid point of the sides of ……………… C (4, 3).

Question 3:

Find the center of the circle …………… C (3, 11).

Question 4:

…………………..

…………………..

…………………..

Question 20:

A (2, 2), B (-2, 4), C(2, 6) are the vertices of a triangle ABC. Prove that ABC is an isoceles triangle.

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Exe-11(b),

OP Malhotra Coordinate Geometry Class-10 S.Chand ICSE Maths Solutions Ch-11

Question 1:

Find the slop of a line whose inclination to the positive ………….. is given as :

(i) 30

(ii)……….

Question 2:

Find the slop ……………….. and (√3, 3)

Question 3:

The side BC of an …………. of its sides ?

Question 4:

………………….

…………………..

……………………

Question 16:

If the point (x, 1), (1, 2) and ……………….. = 1.

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Exe-11(c),

OP Malhotra Coordinate Geometry Class-10 S.Chand ICSE Maths Solutions Ch-11

Question 1:

State the slop of the line

(i)……………

………………

Question 2:

Given 3x + 2y + 4 = 0

(i)………………

…………………..

Question 3:

State the equation of line which has the y-intercept

(a)……………

…………………

Question 4:

……………………

,…………………..

…………………….

Question 21:

(i) Write down the coordinate  of the ……………. in the ratio 1 : 2

(ii) Calculate the distance ……………….. is the origin.

(iii) In what does ……………. line AB  ?

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Self Evaluation And Revision

OP Malhotra Coordinate Geometry Class-10 S.Chand ICSE Maths Solutions Ch-11

Question 1:

(a) The mid- point pf the …………. of AB

(b) Match the equations ………………… y = 2.

(c) Write down the equation of the line whose ………………. ratio 2 : 3

Question 2:

(a) Calculate the distance ……… is 11.

(b) (i) The ………. of A.

(ii) Determine the …………….. 4x – 3y + 12 = 0.

Question 3:

……………………

……………………

…………………..

Question 27:

(a) The slop of a line …………. Find

(i) K

(ii) Midpoint …… in (i).

(b) ………………..

— : End of Coordinate Geometry OP Malhotra S Chand Solutions :–

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Return to :-   OP Malhotra S Chand Solutions for ICSE Class-10 Maths

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