Chapter 1.3, Problem 23PPS

To determine

To find the distance.

Answer to Problem 23PPS

Distance between points is $4\sqrt{13}$ .

Explanation of Solution

Given information:

  $X(-3,-6)$ and $Y(5,6)$

Formula used:

Distance between pair of points= $\sqrt{{(x_2^{}-x_1^{})}^2+{(y_2^{}-y_1^{})}^2}$

Calculation:

Let

  $x_1^{}=-3,x_2^{}=5$ and,

  $y_1^{}=-6,y_2^{}=6$

Substituting values,

  $XY=$$\sqrt{{(5-(-3))}^2+{(6-(-6))}^2}$

Solving,

  $XY=\sqrt{{(5+3)}^2+{(6+6)}^2}$

So,

  $XY=$$\sqrt{8^2+{12}^2}$

And $XY=\sqrt{64+144}$

Factoring,

  $XY=\sqrt{208}$

Now,

  $XY=\sqrt{2\times 2\times 2\times 2\times 13}$

Hence, distance between points is $4\sqrt{13}$ .