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5-Minute Check

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1.3 Use Midpoints & Distance Formulas Students will analyze segments and determine lengths in the coordinate plane. Why? So you can solve real world problems dealing with length, as seen in Ex 1. Mastery is 80% or better on 5-min checks and indy practice.

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VOCABULARY Midpoint: The point that divides a segment into two congruent segments Segment bisector: A point, ray, line, line segment, or plane that intersects the segment at its midpoint

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Example 1 Find segments lengths RS= _RT_ + _TS_Segment Addition Postulate = _21.7_ + _21.7_Substitute. RS = _43.4._ Add. Find RS Solution Point _T_ is the midpoint of RS. So, RT = _TS_ = 21.7.

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Guided Practice…..White Boards Answer 4 1/2 Find CB Find AB Answer 2 1/4

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Quick Write If B is between AC and collinear is it a midpoint? Explain

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Example 2 Use algebra with segment lengths BC = CDWrite equation. _3x – 2_ = _2x + 3_Substitute. _x – 2_ = _3_Subtract _2x_ from each side. x = _5_Add _2_ to each side. Step 2 Evaluate the expression for BC when x = _5_ BC = _3x – 2_ = _3(5) – 2_ = _13_ So, the length of BC is _13_. Write and solve an equation.

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Think….Ink…..Share Point K is the midpoint of JL. Find the length ofJL 8-3x=2x+5 8=5x+5 3=5x X=3/5……plug in to solve JL = 12 2/5

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On Your Own Page 19 # 1-16 All

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5-Min Check 1. What does it mean to bisect a segment? Simply put, it cuts a segment in half. 2. Line l bisects segment AC at point B. If segment AC is 19 cm, what is the measure of BC? 9.5 cm 3. M is the Midpoint of AC. If AM is x+5 and MC is 2x, what is the length of AM? 10

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THE MIDPOINT FORMULA The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y- coordinates of the endpoints. If A(x 1,y 1 )and B(x 2, y 2 ) are points in a coordinate plane, then the midpoint M of AB has coordinates

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Guided …Example 3 Use the Midpoint Formula The end points of PR are P(–2, 5) and R(4, 3). Find the coordinates of the midpoint M. The midpoint of AC is M(3, 4). One endpoint is A(l, 6). Find the coordinates of endpoint C. X1 X2 2 Y1Y2 2

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Midpoints Cont.. The coordinates of the midpoint of PR are (1,4)

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Guided….Endpoint Option 1 & 2 The midpoint of XZ is M(5, –6). One endpoint is X(–3, 7). Find the coordinates of endpoint Z Step 1 Find x. M = (X1 +X2) Substitute for what we know. 2 Step 2 Find y. M = (Y1 + Y2) Substitute for what we know. 2

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Distance Formula

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Think…Ink…Share What is the approximate length of RT, with endpoints R(3, 2) and T(–4, 3)? Solution Sq Root of 50 Or 7.07

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What was the Objective for today? Students will analyze segments and determine lengths in the coordinate plane. Why? So you can solve real world problems dealing with length, as seen in Ex 1. Mastery is 80% or better on 5-min checks and indy practice.

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Assignment Page 19-20 # 18-34 all

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