Midpoint and Distance Formula

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

• $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

• $\left(\frac{x_1-x_2}{2},\frac{y_1-y_2}{2}\right)$

• $\left(\frac{x_1+y_1}{2},\frac{x_2+y_2}{2}\right)$

• $\left(\frac{x_2-x_1}{2},\frac{y_2-y_1}{2}\right)$

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

• $d=\sqrt{\left(x_1+y_1\right)^2-\left(x_2+y_2\right)^2}$

• $d=\sqrt{\left(x_1-y_1\right)^2-\left(x_2-y_2\right)^2}$

• $d=\sqrt{\left(x_1+x_2\right)^2-\left(y_1+y_2\right)^2}$

• $d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$

What is the MIDPOINT of the segment?

• $\left(-3,4\right)$

• $\left(5,4\right)$

• $\left(1,4\right)$

• $\left(4,1\right)$

What is the HORIZONTAL distance between the two points?

• -3

• 8

• 4

• 5

• 9

What is the MIDPOINT of the segment?

• $\left(2,7\right)$

• $\left(2,-5\right)$

• $\left(1,2\right)$

• $\left(2,1\right)$

What is the VERTICAL distance between the two points?

• 12

• 6

• 7

• 2

• 13

Using the Midpoint Formula, which is the correct setup to find the MIDPOINT for the endpoints:

 (4, 3) and (2, 7)

•  $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{4+2}{2},\frac{3+7}{2}\right)$  

•  $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{4+3}{2},\frac{2+7}{2}\right)$  

•  $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{3+7}{2},\frac{4+2}{2}\right)$  

Using the Distance Formula, which is the correct setup to find the distance between the two points:

 (4, 3) and (2, 7)

•  $d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}=\sqrt{\left(4-3\right)^2+\left(2-7\right)^2}$  

•  $d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}=\sqrt{\left(4-2\right)^2+\left(3-7\right)^2}$  

•  $d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}=\sqrt{\left(4-7\right)^2+\left(3-2\right)^2}$  

Using the Midpoint Formula, which is the correct setup to find the MIDPOINT for the endpoints:

 (−5, 1) and (8, −9)

•  $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{1+\left(-9\right)}{2},\frac{-5+8}{2}\right)$  

•  $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{-5+1}{2},\frac{8+\left(-9\right)}{2}\right)$  

•  $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{-5+8}{2},\frac{1+\left(-9\right)}{2}\right)$  

Using the Distance Formula, which is the correct setup to find the distance between the two points:

 (−5, 1) and (8, −9)

•  $d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}=\sqrt{\left(-5-8\right)^2+\left(1-\left(-9\right)\right)^2}$  

•  $d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}=\sqrt{\left(-5-1\right)^2+\left(8-\left(-9\right)\right)^2}$  

•  $d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}=\sqrt{\left(-5-\left(-9\right)\right)^2+\left(8-1\right)^2}$