Question

Finding distance between each pair of points. how to know which is x1 y1 and x2 y2 when using (x2-x1)^2 + (y2-y1)^2? People are saying it doesnt matter but wouldnt it be different if you answered it but switched them up?

Answer 1

It doesn't matter what order the coordinates are in the distance formula as long as it stays in it's corresponding order. In this case, (-7,5) could be (x1,y1) and (3,-5) could be (x2,y2) or vise versa, just as long as you don't mix up the coordinates (so no (-7,-5) or (3,5)). I'll demonstrate this below:

$\sqrt{(-7-3)^2+(5-(-5))^2}\\\sqrt{(-10)^2+(10)^2}\\\sqrt{100+100}\\\sqrt{200}\\\\\sqrt{(3-(-7))^2+(-5-5)^2}\\\sqrt{(10)^2+(-10)^2}\\\sqrt{100+100}\\\sqrt{200}$

The distance between these points, no matter the order, is √200, or approximately 14.14 units.