Question

Find the distance between (4,-17) and (-5,10). Make sure you fully simplify your radical answer

I need help explaining what to do here. Any help is much appreciated!

Answer 1

Answer:
`9√(10)`

This is the same as writing 9*sqrt(10)

Work Shown

`(x_1,y_1) = (4,-17) \text{ and } (x_2, y_2) = (-5,10)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2) = \text{distance formula}\\\\d = √((4-(-5))^2 + (-17-10)^2)\\\\d = √((4+5)^2 + (-17-10)^2)\\\\d = √((9)^2 + (-27)^2)\\\\d = √(81 + 729)\\\\d = √(810)\\\\d = √(81*10)\\\\d = √(81)*√(10)\\\\d = 9√(10)\\\\d \approx 28.460499\\\\`

For more help and examples, search out "distance formula". I recommend doing an image search if you are a visual learner. The pythagorean theorem is another approach. In fact, the distance formula is a modified special case of the pythagorean theorem.