Question

Which expression gives the distance between the points (2,4) and (-4,8)?

Answer 1

(y2-y1)/(x2-x1)=(8-4)/(-4-2)

Answer 2

`√((2+4)^2+(4-8)^2)`

Explanation:

From the options you can see that there´s only one option that could actually give you the length of a segment between two points which are the third and foruth options now remember the formula for segments between two points, which what basically does is calculating the hypothenuse between the two of them:

`c^2= a^2+b^2\\c^2= (x1-x2)^2+(y1-y2)^2\\`

Now we just insert the values into the formula:

(2,4) (-4,8)

`c^2= a^2+b^2\\c^2= (x1-x2)^2+(y1-y2)^2\\c^2=(2-(-4))^2+(4-8)^2\\c=√((2+4)^2+(4-8)^2)`