#### Read Microsoft PowerPoint - 1-3 Distance, midpoint, and slope text version

`Lesson 1-3FormulasLesson 1-3: Formulas 1The Coordinate PlaneDefinition: In the coordinate plane, the horizontal number line (called the x- axis) and the vertical number line (called the y- axis) interest at their zero points called the Origin.y - axisOrigin x - axisLesson 1-3: Formulas2The Distance FormulaThe distance d between any two points with coordinates ( x1 , y1 ) and ( x2 , y2 ) is given by the formula d = ( x - x ) 2 + ( y - y .2 1 2)2 1Example: Find the distance between (-3, 2) and (4, 1) x1 = -3, x2 = 4, y1 = 2 , y2 = 1d= d= d=(-3 - 4) + (2 - 1)2 222(-7) + (1) = 49 + 150 or 5 2 or 7.07Lesson 1-3: Formulas 3Midpoint FormulaIn the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates ( x1 , y1 ) and ( x2 , y2 ) are  x1 + x2 , y1 + y2  .   2 2 Example:Find the midpoint between (-2, 5) and (6, 4)x1 = -2, x2 = 6, y1 = 5, and y2 = 4M= M= -2 + 6 , 5 + 4   2 2   4 , 9  =  2, 9   2 2  2Lesson 1-3: Formulas 4Slope FormulaDefinition: In a coordinate plane, the slope of a line is the ratio of its vertical rise over its horizontal run. rise run Formula: The slope m of a line containing two points withcoordinates ( x1 , y1 ) and ( x2 , y2 ) is given by the formula m =y2 - y1 where x1  x2. x2 - x1Example: Find the slope between (-2, -1) and (4, 5).x1 = -2, x2 = 4, y1 = -1, y2 = 5y2 - y1 5 - ( -1) m= = x2 - x1 4 - (-2)6 m = =1 65Lesson 1-3: FormulasDescribing LinesLines that have a positive slope rise from left to right. Lines that have a negative slope fall from left to right. Lines that have no slope (the slope is undefined) are vertical.Lines that have a slope equal to zero are horizontal.Lesson 1-3: Formulas6Some More ExamplesFind the slope between (4, -5) and (3, -5) and describe it. m=-5 - -5 0 = =0 4-3 1Since the slope is zero, the line must be horizontal. Find the slope between (3,4) and (3,-2) and describe the line. 4 - -2 6 = = m=3- 3 0Since the slope is undefined, the line must be vertical.Lesson 1-3: Formulas 7Example 3 : Find the slope of the line through the given points and describe the line. (7, 6) and (­ 4, 6)ySolution: y 2 - y1 m =x2 - x1left 11 (-11)up 0 (­ 4, 6) (7, 6)x6-6 = ( - 4) - 7 0 = - 11 =0 This line is horizontal.Lesson 1-3: Formulas8Example 4: Find the slope of the line through the given points and describe the line. (­ 3, ­ 2) and (­ 3, 8) Solution: m= 8 - ( -2 ) = ( - 3) - ( - 3 ) = 10 0 y 2 - y1 x 2 - x1right 0y(­ 3, 8) up 10x(­ 3, ­ 2)undefinedThis line is vertical.Lesson 1-3: Formulas 9PracticeFind the distance between (3, 2) and (-1, 6). Find the midpoint between (7, -2) and (-4, 8). Find the slope between (-3, -1) and (5, 8) and describe the line. Find the slope between (4, 7) and (-4, 5) and describe the line. Find the slope between (6, 5) and (-3, 5) and describe the line.Lesson 1-3: Formulas 10`

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