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COORDINATE PLANE

This guide covers the fundamentals of coordinate geometry, including the Cartesian plane, quadrants, and how to describe points using ordered pairs. Learn to calculate the distance between two points using the distance formula, along with practical examples for clarity. Additionally, explore finding the midpoint of a segment by averaging the coordinates of its endpoints. Step-by-step instructions help simplify complex concepts, making this resource ideal for students wishing to master these essential geometry skills.

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COORDINATE PLANE

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  1. COORDINATE PLANE

  2. Coordinate plane Quadrant I (+, +) Quadrant II (-, +) y-axis origin x-axis (0,0) Quadrant III (-, -) Quadrant IV (+, -)

  3. Coordinate Geometry Describe a point with an ordered pair (x, y) Finding Distance Use two points and the distance formula d = (x2 – x1)2 + (y2 – y1)2 d is the distance of two points A(x1,y1) and B(x2,y2)

  4. Lets see how it works! AB has endpoints A(1,-3) an B(-4,4). Find AB to the nearest tenth. Label your points A( 1, -3 ) B ( -4, 4 ) x1 y1 x2 y2 (-4 -1)2 +( 4 – (-3))2 -52 + 72 25 + 49 74 8.6

  5. Let’s put this in the calculator: Punch in: ( ( -4 - 1 ) 2 + ( 4 - ( -3 ) ) 2 )

  6. Your Screen should look like this: ((-4 – 1 )2 + (4 – ( -3 ))2) Let’s Try another: The distance between point A (2, -1) and B (2, 5) First label points x1 y1 x2 y2 Second put into distance formula (2 – 2)2 + (5 – (-1))2 Punch into the calculator 6

  7. Assignment Page46 Problems 1 – 17

  8. FINDING MIDPOINT OF A SEGMENT

  9. A 7 B 15 11 To find the midpoint of a segment we get the average or mean of the two points Simply we add the two points together and divide by 2 Example 7 + 15 2 22/2 11

  10. When this line is on the coordinate plane we have to take into consideration both the x and the y coordinates E (-2, -3) F (2, 3 ) x1, y1 x2, y2 Formula: x1 + x2 , y1 + y2 2 2 -2 + 2 -3 + 3 2 2 (0, 0) F E

  11. TRY THIS: Find the coordinates of the midpoint of XY with endpoints X(2, -5) and Y ( 6,13) Label points x1, y1 x2, y2 Do we need to see this on a coordinate plane? Use Formula x1 + x2 y1 + y2 2 2 2 + 6 -5 + 13 2 2 (4, 4)

  12. Finding an endpoint The midpoint of XY has coordinates (4, -6), X has the coordinates (2, -3) Find the Y coordinates Let the coordinates of X be x1,y1 Use the midpoint Formula and solve for each coordinate 4 = 2 + x2 2 -6 = -3 + y2 2 -12 = -3 + y2 -9 = y2 endpoint Y (6, -9) 8 = 2 + x2 6 = x2

  13. Assignment Page 46 Problems 18 – 31 32 – 40 for midpoint only 44- 46

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