Question

Find the distance between the points with the given coordinate.

$\mathbf{(}\mathbf{-}\mathbf{4}\mathbf{,}\mathbf{-}\mathbf{6}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{-}\mathbf{7}\mathbf{,}\mathbf{1}\mathbf{)}$

Short answer

The distance between the coordinates$(-4,-6)$ and $(-7,1)$is 5 units.

Step-by-step solution

Step 1. State the concept of ‘Distance between two points in 2 dimensional plane’.

Let the two points in 2 dimensional plane be $(x_1,y_1)$and $(x_2,y_2)$.

The distance between the points is given as:

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}\dots \left(1\right)$

Where $d$is the distance.

Step 2. Calculate the distance.

The two points which is given are $(-4,-6)$and $(-7,1)$.

Substitute $(-4,-6)$as $(x_1,y_1)$and $(-7,1)$as $(x_2,y_2)$in $\left(1\right)$to calculate the distance.

$\begin{array}{l}d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}\\ =\sqrt{{(-7-(-4))}^2+{(1-(-6))}^2}\\ =\sqrt{{(-7+4)}^2+{(1+6)}^2}\\ =\sqrt{{(-3)}^2+{\left(7\right)}^2}\\ =\sqrt{9+49}\\ =\sqrt{58}\end{array}$

Step 3. State the conclusion.

Therefore, distance between the points$(-4,-6)$ and $(-7,1)$is$\sqrt{58}$ units.