Chapter 2.1 - Distance

Chapter 2.1 - Distance

​Distance Formula

• ​Distance can be found by picturing a right triangle

• ​Find points with |A – B| or |B – A|

• ​Horizontal leg of the triangle can be found |x₂ – x₁|

• ​Vertical leg of the triangle can be found |y₂ – y₁|

Multiple Choice

What is the distance between the two points: (-5, 1) and (7, -3)?

First, we need to identify x₁, x₂, y₁, and y₂. Which is correct?

• (-5, 1) and (7, -3)

  (x₁, y₁) and (x₂, y₂)

• (-5, 1) and (7, -3)

  (x₁, x₂) and (y₁, y₂)

• (-5, 1) and (7, -3)

  (y₁, x₂) and (y₂, x₁)

• (-5, 1) and (7, -3)

  (x₁, y₂) and (x₂, y₁)

Multiple Choice

What is the distance between the two points: (-5, 1) and (7, -3)?

Next, we need to use the distance formula. What is it?

• $$\sqrt[]{\left(x_2-x_2\right)^2+\left(x_1-x_1\right)^2}$$  

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

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

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

Multiple Choice

What is the distance between the two points: (-5, 1) and (7, -3)?

Next, we need to plug the points into the distance formula. What is it?

• $$\sqrt[]{\left(7-5\right)^2+\left(-3-1\right)^2}$$  

• $$\sqrt[]{\left(7-y\left(-5\right)\right)^2+\left(-3-1\right)^2}$$  

• $$\sqrt[]{\left(-3-1\right)^2+\left(7-5\right)^2}$$  

• $$\sqrt[]{\left(-5-7\right)^2+\left(-1-3\right)^2}$$  

Multiple Choice

What is the distance between the two points: (-5, 1) and (7, -3)?

When we do the math, we get $$\sqrt[]{160}$$  . What is the exact answer?

• $$\sqrt[]{160}$$  

• $$12.65$$  

• $$16\ \sqrt[]{10}$$  

• $$4\ \sqrt[]{10}$$