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# G.1 Distance and Midpoint

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### G.1 Distance and Midpoint

1. 1. Distance and Midpoints<br />
2. 2. Engage…<br />A team of archaeologists is studying the ruins of Lignite, a small mining town from the 1800's. They plot points on a coordinate plane to show exactly where each artifact is found. They are using this coordinate plane as a map of a section of the town. It shows the location of a medicine bottle M, a doorknob D, and a pottery jug J . <br /> How far apart is the doorknob and the medicine bottle? How far apart is the Medicine and the Jug? So approximately far apart is the doorknob and the jug? <br />J<br />D<br />M<br />
3. 3. Explore<br />To find the distance from point A to point B you could use the Pythagorean Theorem a2 + b2 =c2<br /> Point A is (1,6), point C is (1,1) and point B is (7,1)<br />A<br />C<br />B<br />
4. 4. OR you can combine some steps and notice you have derived the distance formula<br />Where point one is denoted (x1,y1) and point two is denoted (x2,y2) <br />
5. 5. Distance Problems…<br />Using the figure, if VZ=4a+3 and VW=15-2a.  <br />Find RT for R(-2, 5) and T(-3, -6). Round to the nearest tenth <br />Example 2 Find Distance on a Coordinate Plane<br />Find the distance between A(4, 2) and B(-6, 4). <br />Use the number line to find QR.<br />
6. 6. Midpoint<br />To find the MIDPOINT BETWEEN POINTS YOU CAN USE THE MIDPOINT FORMULA …<br />MIDPOINT- Is the center point located equidistant from the endpoints!!<br />Think of midpoint as an average between the two points<br />
7. 7. NOW FIND THE MIDPOINTS<br />Using the figure, if VZ=4a+3 and VW=15-2a.  <br />Find the coordinates of C if B(2, 4) is the midpoint of and A has coordinates (6, 8)<br />Find RT for R(-2, 5) and T(-3, -6). Round to the nearest tenth <br />Find Distance on a Coordinate Plane<br />Find the distance between A(4, 2) and B(-6, 4). <br />Use the number line to find QR.<br />
8. 8. EXAMPLES-EVALUATE…<br />TO STUDY ON YOUR OWN FOR TEST…<br />http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-07-829637-4&title=ct&chapter=1&headerFile=6&state=ut<br />http://www.csupomona.edu/%7Ejmariappan/dolce/midpoint.htm<br />