OP Malhotra Class-11 Coordinates Basic Concepts of Point S.Chand ISC Maths

Coordinate Geometry Terms
Coordinate Geometry Definition	It is one of the branches of geometry where the position of a point is defined using coordinates.
What are the Coordinates?	Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
Coordinate Plane Meaning	A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Distance Formula	It is used to find the distance between two points situated in A(x1,y1) and B(x2,y2)
Section Formula	It is used to divide any line into two parts, in m:n ratio
Mid-Point Theorem	This formula is used to find the coordinates at which a line is divided into two equal halves.

Equation of a Line in Cartesian Plane

Equation of a line can be represented in many ways, few of which is given below-

(i) General Form

The general form of a line is given as Ax + By + C = 0.

(ii) Slope intercept Form 

Let x, y be the coordinate of a point through which a line passes, m be the slope of a line, and c be the y-intercept, then the equation of a line is given by:

y=mx + c

(iii) Intercept Form of a Line

Consider a and b be the x-intercept and y-intercept respectively, of a line, then the equation of a line is represented as-

y = mx + c

Slope of a Line: 

Consider the general form of a line Ax + By + C = 0, the slope can be found by converting this form to the slope-intercept form.

Ax + By + C = 0 ⇒ By = − Ax – C

By = − Ax – C

or,

⇒y=−A/Bx–C/B

Comparing the above equation with y = mx + c,

m=−A/B

Thus, we can directly find the slope of a line from the general equation of a line.

 Cartesian Plane

A Cartesian plane is a plane which is formed by two perpendicular lines known as the x-axis (vertical) and the y-axis (horizontal). The exact position of a point in Cartesian plane can be determined using the ordered pair (x, y).

 Need of Coordinate Geometry:

Coordinate geometry has various applications in real life. Some of the areas where coordinate geometry is an integral part include.

• In digital devices like computers, mobile phones, etc. to locate the position of cursor or finger.
• In aviation to determine the position and location of airplanes accurately.
• In maps and in navigation (GPS).
• To map geographical locations using latitudes and longitudes.

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Exe-15 (a)

OP Malhotra Class-11 Coordinates Basic Concepts of Point S.Chand ISC Maths

Page 15-3

Question 1:

Update soon

Question 2:

……………

Question 3:

What will a point lie if (i0 its coordinate is 3 rd (ii) its abscissa is zero ?

Question 4:

Where will a point ……………………. positive ordinate.

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Exe-15 (b)

OP Malhotra Class-11 Coordinates Basic Concepts of Point S.Chand ISC Maths

Page 15-9 to 15-10

Question 1:

Find the min point of the line joining.

…………………..

Question 2:

…………………….

………………………

……………………..

Question 15:

Find the …………………….. and (o, 8)

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Exe-15 (c)

OP Malhotra Class-11 Coordinates Basic Concepts of Point S.Chand ISC Maths

Page 15-13

Question 1:

Find the area of triangle whose ……………

…………………..

Question 2:

…………………….

…………………..

……………………..

Question 7:

The straight lines y = …………………….. if c1 = c2

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Chapter Test

OP Malhotra Class-11 Coordinates Basic Concepts of Point S.Chand ISC Maths

Page 15-16

Question 1:

Show that the points (4, 4), …………….. vertices of a right triangle.

Question 2:

………………………

………………………..

……………………….

Question 5:

Find the third vertex of a triangle………………….. these vertices meet at (0, -3)

-: End of Coordinates Basic Concepts of Point Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-11 Maths Solutions

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