What is the distance between (-21/2, -3) and (1, -3)?

Question

I need help with math, history, and english.  I'm preparing for my ACT.

Answer 1

Hi Shannon, since the distance from -3 to -3 is 0, you know that the distance here is only between -21/2 and 1. Which is 1- -(21/2) = 11.5

 

You can confirm this another way, because these sorts of questions usually require using the pythagorean theorem. a^2+b^2=c^2. The distance from [-21/2, 1] = a = 1--(21/2) = 23/2. The distance from [-3, -3] = -3--3 = 3-3 = 0. Therefore, to find c^2 we take (23/2)^2 + 0^2 = 529/4, and we take the square root of this to find c, which is the distance between the two points. sqrt(529/4) = 11.5.

 

You can verify this method by plotting those two coordinates on an x,y coordinate grid. Join them with a diagonal line and then create a right triangle with that line as the hypotenuse. You'll find that the bottom line is the distance from the x coordinates and the vertical distance is the distance in the y coordinates. Again, since this problem has a vertical distance of zero, we only find the distance between the x coordinates by subtracting the two.