Question

What is the distance between the points 5 and negative 3 and 0,2

Answer 1

`5√(2)`

Explanation:

To find distance, it's like using Pythagorean theorem, except with coordinate points. You just need to find the lengths of the sides.
Formula:
`d=\sqrt{(x_1-x_(2))^2+(y_1-y_2)^2 }`
This is because
`a^2+b^2=c^2`, so to find d, the c, you need the square root of a^2 + b^2 (which are the differences between the coordinate points.)

1. (5, -3) and (0, 2) -->
   `d=√((5-0)^2+(-3-2)^2) d=√(5^2+(-5)^2)d=√(25+25)\\ d=√(50) d=5√(2)`
   
   Explanation: Plug in x1, x2, y1, and y2 into the distance formula. Then solve. root 50 is not a perfect square, but you can factor out root 25, which is a perfect square, and it becomes root 25 * root 2. Root 25 is also just 5, so it becomes 5*root2.
   :)