Distance Formula

Distance in Coordinate

Geometry

Discovering Geometry 5th

Edition

Chapter 10

Coordinate Geometry 9

Isabella is standing on the corner of Seventh
Street and 8th Avenue, and her sister Kayleigh is
on the corner of First Street and 3rd Avenue.
To find her shortest sidewalk route to Kayleigh.
Isabella can simply count blocks. But if Isabella
wants to know her diagonal distance to Kayleigh,
she would need the Pythagorean Theorem to
measure across blocks.

What is the shortest distance from Kayleigh to
Isabella?

Describe how you would identify and find the
value of this distance?

Open Ended

What is the shortest distance from Kayleigh to Isabella? 

Describe how you would identify and find the value of this distance?

Practice

Simplifying Square Roots

Match

Match the following

• $$\sqrt[]{81}$$  

• $$\sqrt[]{16}$$  

• $$\sqrt[]{9}$$  

• $$\sqrt[]{144}$$  

• $$\sqrt[]{49}$$  

9

4

3

12

7

• 9

• 4

• 3

• 12

• 7

Multiple Choice

Simplify $$\sqrt[]{20}$$

• $$4\sqrt[]{5}$$

• $$5\sqrt[]{2}$$

• $$2\sqrt[]{5}$$

• $$2\sqrt[]{10}$$

• Already simplified

Multiple Choice

simplify $$\sqrt[]{96}$$

• $$2\sqrt[]{48}$$

• $$7\sqrt[]{2}$$

• $$16\sqrt[]{6}$$

• $$4\sqrt[]{6}$$

• $$2\sqrt[]{24}$$

Distance in the coordinate plane

Draw

Create a right triangle using the segment as the hypotenuse of a right triangle. Find the measurements of the legs by counting the squares in the horizontal and the vertical.

Multiple Choice

Find the distance between each pair of points. Give your answer as a simplified radical. If you need to see an example click on the word help.

• $$\sqrt[]{41}$$

• $$\sqrt[]{17}$$

• $$\sqrt[]{15}$$

• $$3$$

• $$2\sqrt[]{3}$$

Practice

Distance Formula

Multiple Choice

Which equation represents the $$\Delta x$$ of the following two points.

$$\left(-5,1\right)\ and\ \left(-2,-1\right)$$

• $$-5-1$$

• $$-2--1$$

• $$-1-1$$

• $$-2--5$$

• $$5--2$$

Multiple Choice

Which equation represents the $$\Delta y$$ of the following two points.

$$\left(-5,1\right)\ and\ \left(-2,-1\right)$$

• $$-5-1$$

• $$-2--1$$

• $$-1-1$$

• $$-2--5$$

• $$5--2$$

Multiple Choice

Find the distance between the following two points.

• $$\sqrt[]{14}$$

• $$2\sqrt[]{29}$$

• $$2\sqrt[]{10}$$

• $$2\sqrt[]{8}$$

• $$\sqrt[]{37}$$

If you understand it, go to the next slide. ​

​Still confused.

Watch the following video.

Multiple Choice

Find the area and the perimeter of a triangle with vertices at the following points. (-4,8), (3,8), and (3,3). Round your answer to the nearest tenth.

• Area= 17.5

  Perimeter=20.6

• Area=53.3

  Perimeter=33.8

• Area=14.8

  Perimeter=19.2

• Area=22.4

  Perimeter=23.8

Multiple Choice

Find the area and the perimeter of a quadrilateral with vertices at the following points. (-6,-1), (-3,-4), (3,8), and (6,5). Round your answer to the nearest tenth.

• Area=94.7

  Perimeter=57.9

• Area=53.3

  Perimeter=33.8

• Area=27.6

  Perimeter=24.4

• Area=18.4

  Perimeter=48.5

​If you got the wrong answers, watch the following video.