Chapter 1.3, Problem 25PPS

To determine

To find the distance.

Answer to Problem 25PPS

Distance between points is $\sqrt{17}$ .

Explanation of Solution

Given information:

  $X(1,2)$ and $Y(5,9)$

Formula used:

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

Calculation:

Let

  $x_1^{}=1,x_2^{}=2$ and,

  $y_1^{}=5,y_2^{}=9$

Substituting values,

  $XY=\sqrt{{(2-1)}^2+{(9-5)}^2}$

Solving,

  $XY=\sqrt{{(1)}^2+{(4)}^2}$

So,

  $XY=\sqrt{1+16}$

And $XY=\sqrt{17}$

Hence, distance between points is $\sqrt{17}$ .