12/2 Midpoint and Distance Formulas

Given two points (x₁, y₁), (x₂, y₂) the distance between them is:

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Answer explanation

Yes, the y's are first in this picture, but that doesn't matter because we are adding the two parts together...2 + 3 is the same as 3 + 2

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

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Tags

CCSS.HSG.GPE.B.6

Find the distance between the points (4, 3) and (0, 6).

• 6.1

• 12.5

• 5

• (2, 4.5)

Answer explanation

Did you choose 12.5? If so, then you need to use the square root key on a calculator...and not divide by 2.

What is the midpoint between (3, -1) and (7, -5)

• 5.7

• (1, -3)

• (5, -3)

• (2, 2)

What is the midpoint between (3, -1) and (8, -6)

• (1, 1)

• 7.1

• (5.5, -3.5)

• 2.8

Find the distance.

• (6, 4.5)

• 7.8

• 7.9

• 3

Find the distance between ( 1, 3) and (5, 6)

• 2.2

• 12.5

• 5

• (3, 4.5)

What is the midpoint of the segment with endpoints (1, 9) and (-3, 5)?

How would you figure this out?

• $\left(\frac{1+-3}{2},\ \frac{9+5}{2}\right)$

• $\left(\frac{1+9}{2},\ \frac{-3+5}{2}\right)$
  

• $\left(\frac{1--3}{2},\ \frac{9-5}{2}\right)$
  

• $\sqrt{\left(-3-1\right)^2+\left(5-9\right)^2}$
  

Find the distance between the two given points: (3, -2) and (-1, 0).

How would you figure this out?

• $\sqrt{\left(-1-3\right)^2+\left(0--2\right)^2}$

• $\sqrt{\left(3--2\right)^2+\left(-1-0\right)^2}$

• $\sqrt{\left(-1+3\right)^2-\left(0+-2\right)^2}$

• $\left(\frac{3+-1}{2},\frac{-2+0}{2}\right)$

Answer explanation

pay attention to the signs

What is the midpoint of the segment with endpoints (2, 3) and (4, 5)?

How would you figure this out?

•  $\left(\frac{2+4}{2},\ \frac{3+5}{2}\right)$ 

•  $\left(\frac{2+3}{2},\ \frac{4+5}{2}\right)$ 
  

•  $\sqrt{\left(4+2\right)^2+\left(5+3\right)^2}$ 
  

•  $\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}$ 
  

Answer explanation

only 2 of these options were possibilities...the two with the square root sign could not be right...this is asking about MIDPOINT...MIDDLE POINT...(x, y)