# 9 a 0 0 b 12 8 10 r 12 8 s 6 12 13 s 10 22 t 9 10 14

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Find the coordinates of the midpoint of a segment with the given endpoints.9. A(0, 0), B(12, 8)10. R(–12, 8), S(6, 12)13. S(10, –22), T(9, 10)14. K(–11, 2), L(–19, 6)1-3 Study Guide and Intervention(continued)Locating Points and MidpointsMrs. Taylor
NAME ______________________________________________ DATE______________________________ PERIOD ______________Locate PointsThe midpoint of a segment is half the distance from one endpoint to the other. Points located at other fractional distances from one endpoint can be found using a similar method.Locating Points ona Number LineIf the coordinates of the endpoints of a segment are x1and x2and the point ismnof the distance from x1to x2, then the coordinate of the point isx1+m|x2x1|n.Locating Points ona Coordinate PlaneIf a segment has endpoints A(x1, y1) and B(x2, y2) and the point is mnof the distance from point Ato point B, then the coordinates of the point are(x1+m|x2x1|n, y1+m|y2y1|n).Example 1: Find the coordinates of a point 13of the distance from Ato B.The coordinates of A and B are –5 and 2. If Pis the point 13of the distance from Ato B, then the coordinate of Pis5+|2−(−5)|3=−5+73=832.7.Example 2: Find the coordinates of P, a point 14of the distance from A(–2, 4) to B(4, 3).P=(x1+m|x2x1|n, y1+m|y2y1|n)=(2+|4−(−2)|4,4+|3−(−4)|4)¿(2+64,4+74)or about (12,214).ExercisesUse the number line to find the coordinate of the point the given fractional distance from Ato B.1. 153. 234. 346. 25Chapter 119Glencoe Geometry
Find Pon ´NMthat is the given fractional distance from Nto M.7. 15; N(–3, –2), M(1, 1)8. 13;N(–2, –4), M(4, 4)11. 14;N(–2, 5), M(0, –4)12. 25;N(–2, –1), M(8, 3)
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