What is the distance between the points (12,-8) and (-14,20)

The distance between these two points is a diagonal line. In order to solve this problem, you need to plot your points and form a right triangle. The overall distance from one point to another on the x-axis is 26 (12-(-14)), and the overall distance from one point to another on the y-axis is 28 (20-(-8)). These two distances will form a right angle at (-14,-8). The distances on the x and y axis are the 'legs' of the triangle and the distance between the given points in the problem represents the hypotenuse. Using the pythagorean theorem (a^2 +b^2 = c^2), we can substitute in our values of 'a' and 'b' to get 28^2 + 26^2 = c^2, or 784 + 676= 1460, therefor the square root of 1460 is approximately 38.2.

GoddessofDork GoddessofDork · Answer 2 · 2018-12-27T22:51:34+01:00

Steps

Distance formula: [tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] , with (x₁,y₁) and (x₂,y₂) as coordinates.

So to find the distance between these two points, we are going to be plugging them into the Distance Formula and solving as such:

[tex]D=\sqrt{(12-(-14))^2+(-8-20)^2}\\D=\sqrt{(26)^2+(-28)^2}\\D=\sqrt{676+784}\\D=\sqrt{1460}[/tex]

Now, with this radical we can simplify it using the product rule of radicals (√ab = √a × √b) as such:

[tex]\sqrt{1460}=\sqrt{10*146}=\sqrt{5*2*2*73}=2*\sqrt{73*5}=2\sqrt{365}[/tex]

Answer:

In short:

Exact distance: √1460 or 2√365 units
Approximate Distance (rounded to the hundreths): 38.21 units