Question

How do I find the distance between (-2,5) and (22,12)

Answer 1

Answer:

The distance between the two points is 25.

Step-by-step explanation:

In order to find the distance between two points in the coordinate plane, you must first make a right triangle and use the Pythagorean Theorem to solve for the missing side, which is the distance between the points.  Sometimes, it is best to graph the points to get a visual of the triangle, however, you can also find the lengths of the legs ('a' and 'b') by finding the distance between your x and y values.  In this case, there are 24 points between the x-values and 7 points between the y-values.  These represent our legs in the Pythagorean Theorem:  a² + b² = c².  Filling in the values for 'a' and 'b' gives us: 24² + 7² = c² or 576 + 49 = 625.  In order to find c, we need to take the √625, which is 25.  So, the distance between the points given is 25.

Answer 2

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{22}~,~\stackrel{y_2}{12})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[22-(-2)]^2+[12-5]^2}\implies d=\sqrt{(22+2)^2+(12-5)^2} \\\\\\ d=\sqrt{24^2+7^2}\implies d=\sqrt{625}\implies d=25$