Question

distance between (3, -12) and (23, -12).

Answer 1

is it 400

Answer 2

Use the Pythagorean theorem (sometimes called the distance formula for this kind of problem):

\[d^2=(x_2-x_1)^2+(y_2-y_1)^2\rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]plugging in the numbers gives
d=20

An easier way to do this is to notice that the y coordinate doesn't change, so we just have to consider the change in x:
23-3=20

Answer 3

dont you have to square it though?

Answer 4

which part?

Answer 5

the formulas is (x2-x1)^2

Answer 6

No, you are confused. Allow me to draw:this situation requires the Pythagorean theorem ans I gave above, but your points arewhich as you can see does not lead to d being the hypotenuse of a right triangle, so we only need to subtract.

Notice that if you want to use the Pythagorean theorem with this it becomes\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(23-3)^2+(-12-(-12))^2}\]\[d=\sqrt{20^2-0^2}=\sqrt{20^2}=20\]so you get the same answer either way. You could also just see that since the y-component doesn't change the general formula becomes\[d=\sqrt{(x_2-x_1)^2+0}=\sqrt{(x_2-x_1)^2}=x_2-x_1\]So we see that if the y-component stays the same the Pythagorean theorem reduces to a simple difference of x coordinates, so it all works out.