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Published byEstrella Waldron Modified over 2 years ago

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COORDINATE PLANE

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y-axis (0,0) Coordinate plane

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We can use pythagorean theorem to find distance in the coordinate plane

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Coordinate Geometry Describe a point with an ordered pair (x, y) Finding Distance d is the distance of two points A(x 1,y 1 ) and B(x 2,y 2 )

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Use two points and the distance formula d = (x2 – x1)2 + (y2 – y1)2

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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 ) x 1 y 1 x 2 y 2

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Putting in calculator Your Screen should look like this: ((-4 – 1 )2 + (4 – ( -3 ))2)

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Let’s Try another: The distance between point A (2, -1) and B (2, 5) First label points x 1 y 1 x 2 y 2 Second put into distance formula (2 – 2) 2 + (5 – (-1)) 2 Punch into the calculator

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Assignment Page 46 Problems 1 – 17

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FINDING MIDPOINT OF A SEGMENT

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A 7 B 15 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 22/211

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When this line is on the coordinate plane we have to take into consideration both the x and the y coordinates E F E (-2, -3)F (2, 3 ) x 1, y 1 x 2, y 2 Formula: x 1 + x 2, y 1 + y 2 2 2 -2 + 2 -3 + 3 2 2 (0, 0)

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TRY THIS: Find the coordinates of the midpoint of XY with endpoints X(2, -5) and Y ( 6,13) Label points x 1, y 1 x 2, y 2 Do we need to see this on a coordinate plane? Use Formula x1 + x2 y1 + y2 2 2

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Find the midpoint of AB A = (0, 0) B = (8, 4)

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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 x 1,y 1 Use the midpoint Formula and solve for each coordinate 4 = 2 + x 2 2 -6 = -3 + y 2 2 endpoint Y (6, -9)

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Given the coordinate point A and the midpoint of AB has coordinates (5, -8). Find the coordinates of point B A b

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Assignment Page 46 Problems 18 – 40 EVEN 44 & 46

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