Question

distance of point (-5,+12) from origin is​

Answer 1

Answer:

Method 1.

Let the point plotted on the cartesian plane (coordinate system).

Since abscissa(x-coordinate) is negative'

The point will be on the left of Y-axis.

Since ordinate(y-coordinate) is positive,

The point will lie above X-axis.

Hence the point lies in 3rd quadrant.

Now the point is 5 units left side from Y-axis and 12 units above the X-axis.

Now the dist 5 and 12 form perpendicular sides of triangle where the required distance is hypotenuse. (pls draw diagram and then analyse).

Using Pythagoras theorem we can say required distance(hypotenuse.) =square root ( 5^2+12^2)

=square root(25+144)= square root (169)=13.

ANS=13.

METHOD 2.

Distance between any two points is given by,

Dist=

$\sqrt{(x1 - x2) ^{2} + (y1 - y2)^{2} }$

Where (x1,y1) and ( x2, y2) are the two points between whose the dist is to be found.

The two points are (-5,12) and(0,0).

Comparing with general points we get x1=-5,

y1=12 , x2=0 , y2=0.

Now applying the formula we get,

Dist= square root[(-5-0)^2+(12-0)^2]

=square root(5^2+12^2).

=square root(25+144).

=square root(169).

=13.

Ans. =13.

(the 2nd method's formula is derived by the 1st method).

Thank you.