Question

The distance of the point $\left( -3,4 \right)$ from the origin is?

Answer 1

Hint: We are asked to find the distance of the point $\left( -3,4 \right)$ from the origin. We need to find the distance of the point $\left( -3,4 \right)$ from the point $\left( 0,0 \right)$ . We will be finding the distance of the points using the formula $\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}$ .

Complete step-by-step solution:
We are asked to find the distance of the point $\left( -3,4 \right)$ from the origin . We will be solving the given question using the distance formula in geometry.
The origin is a special point in geometry that is used as a fixed reference for a notation of a particular point in the surrounding space.
It is usually denoted by the letter O. The coordinates of the origin are always zero. The coordinates are given as follows,
$\Rightarrow O=\left( 0,0 \right)$
The formula to find the distance between any of the points $\left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right)$ in geometry is given as follows,
 $\Rightarrow D\text{istance}=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}$
Here,
${{x}_{1}}$ is the x coordinate of the first point
${{x}_{2}}$ is the x coordinate of the second point
${{y}_{1}}$ is the y coordinate of the first point
${{y}_{2}}$ is the y coordinate of the second point
According to our question, we need to find the distance of the point $\left( -3,4 \right)$ from $\left( 0,0 \right)$ .
In our case,
$\left( {{x}_{1}},{{y}_{1}} \right)=\left( 0,0 \right)$
$\left( {{x}_{2}},{{y}_{2}} \right)=\left( -3,4 \right)$
Substituting the above points in the distance formula, we get,
$\Rightarrow D\text{istance}=\sqrt{{{\left( \left( -3 \right)-0 \right)}^{2}}+{{\left( 4-0 \right)}^{2}}}$
Simplifying the expressions in the brackets, we get,
$\Rightarrow D\text{istance}=\sqrt{{{\left( -3 \right)}^{2}}+{{\left( 4 \right)}^{2}}}$
We know that ${{\left( -3 \right)}^{2}}=9$ and ${{4}^{2}}=16$
Substituting the same in the above equation, we get,
$\Rightarrow D\text{istance}=\sqrt{9+16}$
Simplifying the above equation, we get,
$\Rightarrow D\text{istance}=\sqrt{25}$
We know that the value of $\sqrt{25}=\pm 5$
Substituting the same in the above expression, we get,
$\Rightarrow D\text{istance}=\pm 5$
We know that distance is always a positive value. So, it cannot be negative.
Following the same, we get,
$\therefore D\text{istance}=5$
$\therefore$ The distance of the point $\left( -3,4 \right)$ from the origin is 5 units.

Note: The given question is directly formula based and any mistakes in writing the formula will result in an incorrect solution. We must remember that the value of $\sqrt{{{a}^{2}}}$ is not only $+a$ and but the value is $\pm a$ .