ACT Question: Finding A Midpoint

Question

In the standard (x,y) coordinate plane, what is the midpoint of the line segment that has endpoints (3,8) and (1,−4)?

1. (−2, −12)
2. (−1, −6)
3. (11/2, −3/2)
4. (2, 2)
5. ( 4, −12)

Answer 1

You answer is (2,2).

You find each coordinate by subtracting the individual coordinates and divide by 2.

For example, for the x coordinate....... 3-1= 2 2/2 = 1 So, 3-1 = 1+1 = 2

For the y coordinate........................... 8-(-4) = 12 12/2 =6 So, 8-6 = -4 + 6 = 2

In other words, you are finding the mid-point between each individual coordinate!

Answer 2

mid = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

mid = ((3 + 1) / 2, (8 - 4) / 2)

Answer 3

First of all, note that the ACT gives you 60 math problems to do in 60 minutes. This means that EVERY problem has a one minute solution (more or less). And often times the calculator just slows you down. So let's get busy!

Find the midpoint between (3,8) and (1,−4). Ok. Half of students are gonna panic and say "I forget the midpoint formula! OMG! I can't do this!" False. You don't need a formula. What's half way between the x-values 3 and 1? Well, 2 obvi. What's half way between the y-values 8 and -4? That takes slightly more brain power. There are 12 numbers between 8 and -4, so halfway would be 6 numbers away from either end. Let's do 8 minus 6. So 2 is the y-value in the middle. Answer (2, 2). Boom!