1.3 Use Midpoint and Distance Formulas

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Sec 1-3 Concept: Use Midpoint and Distance Formulas

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1.3 Use Midpoint and Distance Formulas Mrs. vazquez Geometry

G.GPE.7 Essential Question: How do you find the distance and the midpoint between two points on a coordinate plane? Objective: Students will be able to find lengths of segments on a coordinate plane.

Vocab midpoint: point that divides a segment into two ≅segments segment bisector: a point, ray, line, line segment, or plane that intersects the segment at its midpoint

Practice What is the length of BD? x = 6 BD = 52 units 7x + 10 = 9x - 2 -7x +2 -7x +2 What is the length of BD? 12 = 2x x = 6 BD = 9x - 2 BD = 9(6) - 2 BD = 52 units AB is congruent to BD. Therefore AB = BD.

Midpoint Formula If A(x1,y1) & B(x2,y2) are points on a coordinate plane, then the midpoint M is x1+x2 , y1+y2 2 2 Think of midpoint as the average for the x-coordinate & the y-coordinates in an ordered pair.

Use the Midpoint formula to find the coordinates of M. x1+ x2 , y1 + y2 2 2 (-3)+(8) , (5)+(-1) 2 2 5 , 4 2 2 2 5 ,

Distance Formula √(x2- x1)2 + (y2- y1)2 If A(x1,y1) and B(x2,y2) are points on a coordinate plane, then the distance between A & B is √(x2- x1)2 + (y2- y1)2 √(-5 - 3)2 + (6 - 2)2 =√(-8)2 + (4)2 =√64 + 16 = √ 80 = 4√5

Pythagorean Theorem Pythagorean Theorem & the Distance Formula are related. Let a = the distance between the x’s (x2 - x1) Let b = the distance between the y’s (y2 - y1) Let c be the distance of the hypotenuse. Since a2 + b2 = c2, √(a2 + b2) = c.

Apply pythagorean theorem height (a) = 3 units width (b) = 4 units 32 + 42 = c2 9 + 16 = c2 25 = c2 5 = c