Question

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

Answer 1

Steps

• Distance formula: $D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ , 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:

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

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

$\sqrt{1460}=\sqrt{10*146}=\sqrt{5*2*2*73}=2*\sqrt{73*5}=2\sqrt{365}$

Answer:

In short:

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

Answer 2

Answer:

The approximate distance between the points is 38.2

Step-by-step explanation:

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.