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### Course: High school geometry > Unit 1

Lesson 1: Intro to Euclidean geometry# Getting ready for performing transformations

Identifying points, identifying number opposites, estimating angles, and calculating distance help prepare us to perform transformations.

All of math builds on earlier concepts, and geometry is no exception!

Let's refresh some of the earlier concepts that will come in handy as we explore transformations. We'll have links for more practice for any concept in case you would like additional review. Then we'll look ahead to how the idea will help us with transformations.

## Identifying and plotting points on the coordinate plane

### Practice

For more practice, go to Points on the coordinate plane.

### Where will we use this?

There are many ways to transform figures: using a coordinate plane, using a compass and straightedge, folding and layering translucent paper, or using geometry software. Identifying and plotting points will be a building block of transforming on the coordinate plane.

Here are a few of the exercises that build off of the coordinate plane:

## Identifying the opposite of a number

### Practice

For more practice, go to Number opposites.

### Where will we use this?

Reflections across the $x$ -axis or $y$ -axis involve finding the opposite of a number. Rotations by multiples of $90\mathrm{\xb0}$ about the origin also involve number opposites.

Here are a couple of the exercises that build off of number opposites:

## Estimating angle measurement

### Practice

For more practice, go to Estimate angle measures.

### Where will we use this?

We will take our estimations a step further, using positive and negative angle measures to indicate the direction and amount of a rotation. We use this skill in the Rotate points exercise.

Be careful: estimating angle measures only makes sense when our figure is to scale. It is just as important to know when

*not*to estimate as to know when we should.## Calculating distance with the Pythagorean theorem

### Practice

For more practice, go to Distance between two points.

### Where will we use this?

Although translations, reflections, and rotations all preserve distance, dilation generally changes the distance between a point and the center of dilation. We will determine scale factor by comparing distances, and we will create figures with proportional side lengths to the pre-image.

Here are a couple of the exercises that build off of calculating distance:

## Want to join the conversation?

- How will this help me in life?(118 votes)
- Any construction project, like building a dog house.(102 votes)

- How will this help me when i go to the army(33 votes)
- u could use it 2 distract the enemy by saying bet u can't solve this problem😎(154 votes)

**I'm taking HS Geometry next year and am absolutely terrified**(46 votes)- It alright buddy just believe in yourself(36 votes)

- I hate when the teachers set me up on this ;((38 votes)
- pongase a jalar chamaco mi ado(6 votes)

- what is the Pythagorean Theorem?(11 votes)
- side(squared) + side(squared) = Hypotenuse(squared)(20 votes)

- So for finding the distance between two points how will you know which one is a and which one is b when using the Pythagorean Theorem?(2 votes)
- It doesn't matter. The distance from a to b is the same as the distance from b to a, so either point could be either variable.(26 votes)

- How do you use the Pythagorean theorem and make it a correct answer? I messed up on that question and got it wrong 3 times over.(4 votes)
- The formula for distance is fundamentally the same as the Pythagorean Theorem.

This video explains the distance formula:

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/v/distance-formula

This video explains Pythagorean Theorem:

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem

Step 1: form a right triangle. The hypotenuse should connect the two points.

Step 2: Find the lengths of the triangle's legs. This step is represented in the distance formula by the (x2-x1) and (y2-y1) segments and forms the a and b segments of the Pythagorean Theorem

Step 3: Square both numbers. This is done the same way in both of the formulas.

Step 4: Add. This just simplifies both formulas.

Step 5: Square root. This is done to isolate the _c_ in the Pythagorean Theorem and is shown in the distance formula

Hope this helps!(16 votes)

- how do you solve the 4th problem(6 votes)
- you use the Pythagorean theorem to solve it.(7 votes)

- How do you solve the distance between the points and make sure your answer is the right answer?(3 votes)
- Pythagorean theorem, a^2+b^2=c^2. you can use a calculator to square the distances if you're unsure

in this case a would be the distance between the points on the y axis and the b would be the distance between the points on the x axis. plug those into the equation and boom(12 votes)

- Where are the lessons explaining Pythagorean theorem?(7 votes)
- use the length og line equation to find the 4th problem(3 votes)