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P.5The Cartesian Plane

- Our goals are to learn
- How to plot points in the Cartesian Plane
- Use the distance formula to find the distance

between two points. - Use the Midpoint formula to find the midpoint of

a line segment. - Find the equation of a circle.
- Translate points in the plane
- Why do you need to know this?
- For something as common as MAP-READING

The Cartesian Plane

- An ordered pair is . . . a pair of two real

numbers x and y, written (x, y), which represents

a point in the Cartesian plane.

ExamplesPlot the ordered pairs on the coordinate

plane.

- (4, -2), (0, 0), (-4, 0), (-5, -5)

ExampleFind the coordinates of the point

- The point is located three units below the x-axis

and two units to the right of the y-axis. - The point is on the x-axis and 10 units to the

left of the y-axis.

ExampleDetermine the quadrant(s) in which (x, y)

is located so that the condition(s) is (are)

satisfied.

- xlt0 and ylt0
- x -4 and y gt 0
- x gt 4
- -x gt 0 and y lt 0
- xy lt 0

Practice Time!

- Now try problems 67 and 69 on your handout.

Use the distance formula to find the length of

the segment.

- (6, -3), (6, 5)
- (-3, -1), (2, -1)
- (8, 5), (0, 20)

Practice Time!

- Now try problem 70 on your handout.

ExamplesFind the length of each side of the

right triangle and show that these lengths

satisfy the Pythagorean Theorem.

ExamplesShow that the points form the vertices

of the polygon

- Parallelogram (0, 1), (3, 7), (4, 4), (1, -2)

Practice Time!

- Now try problems 70 and 72 on your handout.

Use the midpoint formula to find the center of

the segment.

- (6, -3), (6, 5)
- (-3, -1), (2, -1)
- (8, 5), (0, 20)

Practice Time!

- Now try problems 74-75 on your handout.

The equation of a circle

- You need to know the standard form of the

equation of a circle with Center (h, k) and

radius, r - Write the standard form of the equation of the

specified circle - Center (0, 0) radius 5
- Center (5, -6) radius
- Center (3, -2) solution point (-1, 1)
- Endpoints of a diameter (-4, -1), (4, 1)

Find the center and radius, and sketch the circle.

Practice Time!

- Now try problems 76-78 on your handout.

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