Question

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

Answer 1

Steps

• Distance formula:
  `D=√((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=√((12-(-14))^2+(-8-20)^2)\\D=√((26)^2+(-28)^2)\\D=√(676+784)\\D=√(1460)`

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

`√(1460)=√(10*146)=√(5*2*2*73)=2*√(73*5)=2√(365)`

Answer:

In short:

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

Answer 2

The approximate distance between the points is 38.2

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.