91Ó°ÊÓ

The given points are (0,0) and (5, -3).

We have to find the distance between the points.

We will use the distance formula.

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

with$x_1=0,x_2=5,y_1=0\text{and}{y}_2=−3$

$\begin{array}{l}d=\sqrt{{\left(5−0\right)}^2+{\left(−3−0\right)}^2}\left[d=\text{distance}\right]\\ d=\sqrt{{\left(5\right)}^2+{\left(−3\right)}^2}\\ d=\sqrt{25+9}\\ d=\sqrt{34}\end{array}$

So, the distance is$\sqrt{34}$ .

The given points are (3, -2) and (-5, -2).

We have to find the distance between the points.

We will use the distance formula.

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

With$x_1=3,x_2=−5,y_1=−2\text{and}{y}_2=−2$

$\begin{array}{l}d=\sqrt{{\left(−5−3\right)}^2+{\left(−2−\left(−2\right)\right)}^2}\left[d=\text{distance}\right]\\ d=\sqrt{{\left(−8\right)}^2+{\left(−2+2\right)}^2}\\ d=\sqrt{{\left(−8\right)}^2+{\left(0\right)}^2}\\ d=\sqrt{64+0}\\ d=\sqrt{64}\\ d=8\end{array}$

So, the distance is 8.

The given points are (4, 4) and (-3, -3).

We have to find the distance between the points.

We will use the distance formula.

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

with$x_1=4,x_2=−3,y_1=4\text{and}{y}_2=−3$

$\begin{array}{l}d=\sqrt{{\left(−3−4\right)}^2+{\left(−3−4\right)}^2}\left[d=\text{distance}\right]\\ d=\sqrt{{\left(−7\right)}^2+{\left(−7\right)}^2}\\ d=\sqrt{49+49}\\ d=\sqrt{98}\end{array}$

So, the distance is$\sqrt{98}$ .