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  1. %PDF-1.4 %Çì ¢ 5 0 obj > stream xœÕ][“Ý6r~Ÿ_q ç¤ î—ÇìÅŽíÝd×VÊ©dS)íÈòhW—X¶£(ÿ(ÿ2Ý Ðàp¤3 ryÆ.»@6Ð7‚ y8? Ô¤ÍA῵qýêâ￉‡ ~ºPSÎAew¸Ýøæ‹ IßþpñãEš,þC:eûúÕáWOÀD>„Óç¤&)G" ÿMÎ ž¼º¸ü¿ã“¿\üöÉÅ /ô ÿ “¥q?íFÅdX»›¼ÏÞv /› buSÖƒ7‡õ# “‹ƒ Ï÷Œ8N: Þ˜õ#ÖŠŒt yψÁ›8x£6ˆØÎl|± ...

  2. The Distance Formula: c( Find the coordinates of the point on the line >=8 that is 5 units from the point &3,7(. d( Find the coordinates of the point on the line @=4 that is 12 units from the point &3,7(.

  3. The zero 0 divides the positive axis from the negative axis. A point P in the plane R2 is determined by two coordinates. We write P = (x; y). In space R3 nally, we require three coordinates P = (x; y; z), where z usually is thought of as height, the distance from the xy-plane.

  4. Distance, Midpoint, and Slope Formulas. Find the distance between each pair of points. 1) (0, -8), (-6, 0) 3) (4, 3), (-3, 6) 5) (-1, -6), (3, 7) 7) y.

  5. The Euclidean distance between two points P = (x, y, z) and Q = (a, b, c) in space is defined as. Definition: d(P, Q) = p(x − a)2 + (y − b)2 + (z − c)2. Note that this is a definition and not a result. It is motivated by the theorem of Pythagoras, but we will prove the later result in a moment.

  6. The Distance and Midpoint Formulas . Learning Objectives: 1. Use the Distance Formula 2. Use the Midpoint Formula . Examples: . 1. Find the distance between the points (-3,7) and (4,10). 2. Determine whether the triangle formed by points A=(-2,2), B=(2,-1), and C=(5,4) is a right triangle. 3.

  7. The distance between the points (−3, −4) and (q, 5) is 15. Find the possible values of q. 8. The point C has coordinates ( − 5, 4) The point D has coordinates (6, 1) The point E has coordinates (9, − 13) The midpoint of CE is H The midpoint of DE is I. Work out the distance between the points H and I.

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