<h3>
Answer: 7.1</h3>
=========================================================
Explanation:
The two points are (x1,y1) = (1,3) and (x2,y2) = (8,4)
Use the distance formula to get,
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (3-4)^2}\\\\d = \sqrt{(-7)^2 + (-1)^2}\\\\d = \sqrt{49 + 1}\\\\d = \sqrt{50}\\\\d = \sqrt{25*2}\\\\d = \sqrt{25}*\sqrt{2}\\\\d = 5\sqrt{2}\\\\d \approx 7.0710678\\\\d \approx 7.1](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%281-8%29%5E2%20%2B%20%283-4%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-7%29%5E2%20%2B%20%28-1%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B49%20%2B%201%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B50%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B25%2A2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B25%7D%2A%5Csqrt%7B2%7D%5C%5C%5C%5Cd%20%3D%205%5Csqrt%7B2%7D%5C%5C%5C%5Cd%20%5Capprox%207.0710678%5C%5C%5C%5Cd%20%5Capprox%207.1)
Alternatively, you can plot the two points A(1,3) and B(8,4) on the same xy grid. Then plot point C(8,3). Note that C has the same x coordinate as B, and the same y coordinate as A. Triangle ABC is a right triangle, where the 90 degree angle is at point C. The distance from A to B is the same as finding the length of AB, which is the hypotenuse.
This means we can apply the pythagorean theorem to find the hypotenuse AB. The distance formula is a modified version of the pythagorean theorem. Refer to the diagram below.