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ACT Prep: Tutoring Solution43 chapters | 385 lessons

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Lesson Transcript

Instructor:
*Mia Primas*

Mia has taught math and science and has a Master's Degree in Secondary Teaching.

In this lesson we'll define coordinate geometry and learn about formulas that are commonly used in coordinate geometry. You can then take a brief quiz to see what you learned.

There are all sorts of ways that we can find the measurements of lines and angles. We can use rulers to measure lines and protractors to measure angles. In **coordinate geometry** we can use graphs and coordinates to find measurements and other useful information about geometric figures.

Let's start by reviewing the features of coordinate graphs. A coordinate graph is a rectangular grid with two number lines called **axes**. The ** x-axis** is the horizontal number line and the

With coordinate geometry, various geometric figures can be graphed using the coordinates of the figure's vertices (corners). We can use these coordinates along with mathematical formulas to calculate the length, slope, and midpoint of the sides.

The subscripts of 1 and 2 in the formulas are used to distinguish the coordinates of each point. For example, *x* sub 2 is the *x*-coordinate for the second point and tells us where the point is along the *x*-axis. *y* sub 2 is the *y*-coordinate for the second point and tells us where the point is along the *y*-axis.

Check out this example:

Find the slope, length, and midpoint of side *AB* in triangle *ABC*.

To find the slope of side *AB* we'll substitute the coordinates of points *A* and *B* into the slope formula. It is helpful to label the coordinates with *x* sub 1, *x* sub 2, etc. to remember what values to substitute in the formula. The first value for each point is *x*, the second value is *y*. Then we add the subscripts of 1 and 2 for the first and second points. Once the coordinates are labeled, we can substitute them into the slope formula.

The slope of side *AB* is -5/3. The length of side *AB* is the same as the distance between points *A* and *B*, so we can use the distance formula.

When using the distance formula it's very important to follow the order of operations correctly. We find that the distance between points *A* and *B*, which is also the length of side *AB*, equals the square root of 34.You should note that if we were asked to find an angle measurement of the triangle, we could use the length of the sides along with trigonometric formulas.

Lastly, we'll use the midpoint formula to find the midpoint of line *AB*. The midpoint is the point located at the exact center of the line. Keep in mind that it is a point, so the solution will be coordinates, not a single value.

The point (2.5, 2.5) is the midpoint of line *AB*.

**Coordinate geometry** allows us to find measurements of geometric figures that can be graphed with coordinates. Also, remember that a coordinate graph is a rectangular grid with two number lines called **axes**: the ** x-axis** is the horizontal number line and the

When you are finished, you should be able to:

- Describe a coordinate graph and name the two axes
- Calculate the slope and midpoint of a line using the correct formulas
- Determine the distance between two points using the appropriate formula

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ACT Prep: Tutoring Solution43 chapters | 385 lessons

- What Are the Different Parts of a Graph? 6:21
- Coordinate Graph: Definition & Examples
- Graphing Basic Functions 8:01
- Equation of a Line Using Point-Slope Formula 9:27
- Slopes and Tangents on a Graph 10:05
- How to Use The Distance Formula 5:27
- How to Use The Midpoint Formula 3:33
- Abstract Algebraic Examples and Going from a Graph to a Rule 10:37
- Graphing Undefined Slope, Zero Slope and More 4:23
- Graphs of Parallel and Perpendicular Lines in Linear Equations 6:07
- Graphing Absolute Value Equations: Dilations & Reflections 6:08
- How to Graph an Absolute Value and Do Transformations 8:14
- Coordinate Geometry: Definition & Formulas 3:28
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