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NY Regents Exam - Geometry: Help and Review11 chapters | 135 lessons | 8 flashcard sets

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Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, you'll learn what a coordinate plane is and some coordinate plane terminology. You'll also see a few examples of coordinate planes in action. Then, you can test your new knowledge with a brief quiz.

Mrs. Velasquez gave her class a number line to plot different values.

She explained to them that the arrowheads mean that the number line goes on forever. But they're just going to work with the numbers between -10 and 10 today. She told the class that a square is 6 feet long and asked them to plot that measurement on the number line.

Then, she told them that an apple tree dropped 2 apples. She asked them to plot this situation on the number line. The students added that point to their number lines.

Now, Mrs. Velasquez had a trick up her sleeve. She told her students that a triangle has a length of 6 inches and a height of 2 inches. Some students plotted only the length.

Some plotted only the height.

Some tried plotting both values on the same number line.

Mrs. Velasquez told the class that didn't quite work because length and height are different values. The class was stumped, so she asked them, 'What if I added another number line so you can plot both numbers?' She then showed them a picture of a coordinated plane.

A collective, 'Ah!' arose from the students. They now had two number lines that would allow them to plot two different values. Mrs. Velasquez said they would use the number line going left to right to represent length and the one going up and down to represent height. She demonstrated by moving six units to the right on the horizontal number line, then she moved two units up on the vertical number line. She plotted the point where she ended up. She has now plotted the mystery point.

What Mrs. Velasquez did was create a **coordinate plane**, which is an intersection of two number lines. Just like a regular number line, the ones on a coordinate plane could stretch on infinitely. So we can choose a stopping plot on the number lines convenient for a specific situation.

For example, if the triangle's height were 100 inches, Mrs. Velasquez could have made each number line go up to 100. But since she was only going up to 6, number lines ending at 6 were sufficient. The length of a coordinate plane's number lines is known as its **scale**.

For people to use coordinate planes, they need to have a common language. By convention, we normally call the horizontal number line the **x-axis**, and we normally call the vertical number line the **y-axis**.

Notice that the axes cut the coordinate plane into four equal sections, or **quadrants**.

So the point that Mrs. Velasquez plotted above is in quadrant I. The number of units you move along the axes are the point's **coordinates**. Since you moved 6 positive units along the x-axis, the point's x-coordinate is 6. Since you moved 2 positive units along the y-axis, the point's y-coordinate is 2.

To name a point, we use its x-coordinate followed by its y-coordinate in parentheses. For example, this point would be named (6, 2) since 6 is its x-coordinate and 2 is its y-coordinate.

Mrs. Velasquez showed the class this point:

She asked them to name it. After a few seconds counting along the number lines, one student called out '(3, 4).'

Mrs. Velasquez told him he almost had it. After a few more seconds, he smacked his forehead and said, '(4, 3).' He had mistakenly reversed the x- and y-coordinates, but then he remembered that the x-coordinate always goes first when naming a point.

Mrs. Velasquez then tried to trip them up by showing them this point:

One student hesitantly answered, '(3, 1)?'

Mrs. Velasquez smiled and gave her time to catch her error. After a few seconds, she exclaimed, 'Oh! (-3, 1)!' Because the point was three units to the left on the x-axis, its x-coordinate was negative. Mrs. Velasquez also told the class that this point was in quadrant II. She then showed the class one last important point:

She told them that since it was on the 0 of both numbers lines, its coordinates were (0, 0). She also told them that this was called the coordinate plane's **point of origin** because this was the center of the coordinate plane and the point where the number lines meet.

For homework, Mrs. Velasquez had her students measure their bedrooms and plot the measurement on a coordinate plane where the x-axis represents length and the y-axis represents width, both in inches.

Sandra went home and measured her room. It was 10 feet long and 11 feet wide. So she calculated that it had a length of 120 inches and a width of 132 inches.

If she used the same scale Mrs. Velasquez had, she couldn't plot her point because both of her measurements were larger than 10. So she decided to make each axis go up to 140. That way, both of her measurements would fit on the coordinate plane. She could have used a higher maximum value, such as 1,000, but such a large scale didn't make sense when her largest measurement was only 132.

Since 132 is roughly halfway between 120 and 140, she placed her point halfway between 120 and 140 on the y-axis.

She named the point (120, 132) because she had to move 120 positive units along the x-axis and 132 units along the y-axis to place it on the coordinate plane.

A **coordinate plane** consists of two number lines that intersect, one running horizontally, the other running vertically. The horizontal number line on a coordinate plane is known as the **x-axis**. The vertical number line on a coordinate plane is known as the **y-axis**. A point on a coordinate plane is named by its x-coordinate followed by its y-coordinate in parentheses.

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NY Regents Exam - Geometry: Help and Review11 chapters | 135 lessons | 8 flashcard sets

- Parallelograms: Definition, Properties, and Proof Theorems 5:20
- Measuring the Area of a Parallelogram: Formula & Examples 4:02
- What Is a Rhombus? - Definition and Properties 4:24
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- Squares: Definition and Properties 6:52
- Trapezoids: Definition and Properties 4:24
- Measuring the Area of a Trapezoid 4:38
- Using Heron's Formula in Geometry 5:54
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