Question 62902
 QUESTION:

  Which of the following statements are true?
  The point (-2,-3) is in quadrant II of the Cartesian plane.
  The equation 2x-3y=5 is a linear equation.
  The distance between the points (-5,1) and (-7,9) is 2^17
  ^a^2 +b^2=a+b
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ANSWERS:

The point ( -2, -3 )  is in quadrant II of the Cartesian plane.

No, the point ( -2, -3 ) is not in the II quadrant
Explanation: 

In the  I quadrant both the x and y coordinates are positive.
In the  II  quadrant x  coordinate is negative  while y coordinate is +ve.
In the III  quadrant x coordinate is  -ve and y coordinate is -ve.
In the IV    quadrant x coordinate is +ve and  y coordinate is -ve.

So the point ( -2, -3 )  lies in the III quadrant.

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2.The equation 2x-3y=5 is a linear equation.

Explanation:

A linear equation is an equation involving only the sum of constants or products of constants and the first power of a variable.


These equations are called "linear" because they represent straight lines in Cartesian coordinates.

 
A common form of a linear equation in two variables is y = mx + b, 

(e.g. y = 3x + 5the line crosses the y-axis.

Equations involving terms such as x^2, y^(1/3), and (xy )are "non-linear".


The given equation 2x-3y=5 is linear because its terms involves only first power of variable.

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3.The distance between the points (-5,1) and (-7,9) is 2^17


Explanation:

In coordinate geometry the distance between two points is given by  

Distance Formula,  d = square root of {( x1 -x2)^2 + ( y1 - y2 )^2}

here
 
x1= -5
x2= -7
y1= 1
y2= 9

so, d = square root of {( -5 - -7)^2 + (1- 9 )^2}

      = square root of {( -5+ 7)^2 + ( 1-9)^2}

      = square root of {( 2)^2 + ( -8)^2}

      = square root of {(4 + 64 }

      = square root of { 68 }

      = 2 * square root of 17

      = 2 ( 17 )^1/2

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Last Question is not clear.




Regards,

Praseena.

praseenakos@yahoo.co.in