Question

Find the distance between \[\left( 0,-2 \right)\] from the origin.

Answer 1

Hint: In this problem we have to find the distance between the given point (0,-2) from the origin. We assume that the given points, A(0,-2) and the origin O(0,0). That is so simple to find out the distance of the given points through the distance formula. We know that the distance formula is \[d=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\] . We can now find the distance value.

Complete step by step answer:
We know that the given point is \[\left( 0,-2 \right)\].
Here we have to find the distance between the given point and the origin \[\left( 0,0 \right)\]
We can now write the given points as,
\[\left( {{x}_{1}},{{y}_{1}} \right)=\left( 0,-2 \right)\] and \[\left( {{x}_{2}},{{y}_{2}} \right)=\left( 0,0 \right)\]
We know that the distance formula is,
\[d=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\]
By substituting the above values and simplifying them we can get the distance from the given point from the origin. By substituting and simplifying them we get,
\[\begin{align}
  & \Rightarrow d=\sqrt{{{\left( 0-0 \right)}^{2}}+{{\left( 0+2 \right)}^{2}}}=\sqrt{4} \\
 & \Rightarrow d=2units \\
\end{align}\]

Therefore, the distance between the point \[\left( 0,-2 \right)\] and the origin is 2 units.

Note: Students will make mistakes to find the second point where it is given as origin. And they will make mistake in substituting the values \[{{x}_{1}},{{y}_{1,}}{{x}_{2}},{{y}_{2}}\] in the formula. They may interchange and substitute. At the time of interchanging the values of a and y, we may not get the correct solution. We should always remember that the formula to find the value of a distance between two points is \[d=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\]. We should also remember some of the perfect square values to be used in these types of problems.