### About Finding the Distance Between Two Points:

We can find the distance between any two points on the coordinate plane by sketching out a right triangle and using the Pythagorean formula. From this formula, we are able to create a distance formula. This distance formula allows us to quickly find the distance between any two points. We simply label the points, plug in, and simplify.

Test Objectives
• Demonstrate a general understanding of the distance formula
• Demonstrate the ability to calculate a square root
• Demonstrate the ability to simplify a square root
Finding the Distance Between Two Points Practice Test:

#1:

Instructions: find the distance between each pair of points.

$$a)\hspace{.2em}(-3, 1),(2, 13)$$

#2:

Instructions: find the distance between each pair of points.

$$a)\hspace{.2em}(5,1),(-4,7)$$

#3:

Instructions: find the distance between each pair of points.

$$a)\hspace{.2em}(-9,11),(4,4)$$

#4:

Instructions: find the distance between each pair of points.

$$a)\hspace{.2em}(-1,-4), (5,4)$$

#5:

Instructions: find the distance between each pair of points.

$$a)\hspace{.2em}(-2,-2),(-3,-1)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}13$$

#2:

Solutions:

$$a)\hspace{.2em}3 \sqrt{13}$$

#3:

Solutions:

$$a)\hspace{.2em}\sqrt{218}$$

#4:

Solutions:

$$a)\hspace{.2em}10$$

#5:

Solutions:

$$a)\hspace{.2em}\sqrt{2}$$