Question

Distance of the point (- 3, 4) from the origin is:

Answer 1

Hint: We know that in this question we need to use the distance formula between the given point and the origin, so first we state the formula and then will define the two points and then we will use this formula to find the answer.

Complete step-by-step solution -
So, let’s first look at the distance formula between two points,
If the two points are A( a, b ) and B( c, d ) then the formula for calculating distance ‘d’ is:
$D=\sqrt{{{\left( a-c \right)}^{2}}+{{\left( b-d \right)}^{2}}}$
Now we are going to use this formula for finding distance between the two points.
The two points as per the question is P(- 3, 4) and the other one is origin which is O( 0, 0 ),
Let D be the distance between these two points,
Hence, using the above formula we have ,
a = -3
b = 4
c = 0
d = 0
Now putting these values in $D=\sqrt{{{\left( a-c \right)}^{2}}+{{\left( b-d \right)}^{2}}}$ we get,
$\begin{align}
  & D=\sqrt{{{\left( -3-0 \right)}^{2}}+{{\left( 4-0 \right)}^{2}}} \\
 & D=\sqrt{{{\left( -3 \right)}^{2}}+{{\left( 4 \right)}^{2}}} \\
 & D=\sqrt{9+16} \\
 & D=\sqrt{25} \\
 & D=5 \\
\end{align}$
Hence we can see that the distance between the point and the origin is 5.

Note: An alternate method to solve this question is we can draw a right angle triangle from these three points X( -3, 0 ) , Y( -3, 4 ) and O( 0, 0 ). And now to find the distance between OY we can use Pythagoras theorem like: ${{\left( OY \right)}^{2}}={{\left( OX \right)}^{2}}+{{\left( XY \right)}^{2}}$ , and we can see that the answer will be same.