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  • What is the distance of the point (-3, -5 ) from the y-axis?Option: 1 3Option: 2

What is the distance of the point (-3, -5 ) from the y-axis?

Option: 1

3


Option: 2

-3


Option: 3

5


Option: 4

-5


Answers (1)

best_answer

 

 

Coordinate Axes -

Coordinate Axes

The Cartesian coordinate system, also called a rectangular coordinate system, is based on a two-dimensional plane consisting of the x-axis and the y-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant; the quadrants are numbered counterclockwise as shown in figure below 

A two-dimensional plane where the

  • x-axis is the horizontal axis

  • y-axis is the vertical axis

A point in the plane is defined as an ordered pair, (x,y), such that x is determined by its horizontal distance from the origin and y is determined by its vertical distance from the origin.

The distance from a point to the vertical or y-axis is called the abscissa or x-coordinate

Here, OM is x-coordinate

The distance from a point to the horizontal or x-axis is called the ordinate or y-coordinate

Here, PM is y-coordinate

we can represent the point  (3,−1) in the plane by moving three units to the right of the origin in the horizontal direction, and one unit down in the vertical direction.

Conversion Sign of coordinate

Quadrants

XOY

X'OY

X'OY'

XOY'

(I)

(II)

(III)

(IV)

X- coordinate sign

+

-

-

+

Y-coordinate sign

+

+

-

-

Sign of (x, y)

(+, +)

(-, +)

(-, -)

(+, -)

Polar Coordinate of a Point

Consider the figure,

If OP = r and ∠XOP = Θ. Then, the ordered pair of real numbers (r, Θ) called the polar coordinates of the point P.

From the figure

OM = x = r cos Θ

PM = y = r sin Θ

\\\text{Square and add,}\\\\\mathrm{OM^2+PM^2=x^2+y^2=r^2}\\\\\mathrm{\Rightarrow r=\sqrt{x^2+y^2}}\\\\\mathrm{From\;above\;we\;get}\\\\\mathrm{\Rightarrow \tan\theta=\left ( \frac{y}{x} \right )\Rightarrow \theta=\tan^{-1}\left ( \frac{y}{x} \right )}\\\\\mathrm{i.e.\;\;\;\left ( r\cos\theta,r\sin\theta \right )=(x,y)}\\\\\mathrm{and,\;\;\left (\sqrt{x^2+y^2},\tan^{-1}\left ( \frac{y}{x} \right ) \right )=(r,\theta)}\\\\\text{This is the relation between polar coordinate and cartesian coordinate. }

Example: Point (-5, 2) lies in which quadrant.

Solution

From the table, X-coordinate is -ve and Y-coordinate is +ve. So, the point lies on 2nd quadrant.  

Example: A point lies on X-axis at a distance of 10 units from Y-axis, then the coordinates of the point will be 

Solution : 

Given that point lies on X-axis at a distance of 10 units from the Y-axis, so the point may be on the left of the Y-axis or right of the Y-axis. So, X-coordinate will be -10 or +10.

And, point lies on X-axis, so Y-coordinate will be 0.

So, the coordinate of the point will be (-10, 0) or (+10, 0)     

-

 

 

 

 Distance is always positive and distance will be 3 units 

Posted by

vishal kumar

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