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Coordinate Plane Formulas and Concepts: Distance, Midpoint, Slope

Learn essential formulas in the coordinate plane for calculating distances, midpoints, and slopes between points. Understand the characteristics of lines with different slopes and practice solving related problems.

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Coordinate Plane Formulas and Concepts: Distance, Midpoint, Slope

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  1. Formulas Lesson 1-3 Lesson 1-3: Formulas

  2. The Coordinate Plane Definition: 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 - axis Origin x - axis Lesson 1-3: Formulas

  3. d = d = d = The Distance Formula Find the distance between (-3, 2) and (4, 1) The distance d between any two points with coordinates and is given by the formula d = . Example: x1 = -3, x2 = 4, y1 = 2 , y2 = 1 Lesson 1-3: Formulas

  4. M = M = Midpoint Formula In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and are . Find the midpoint between (-2, 5) and (6, 4) Example: x1= -2, x2= 6, y1 = 5, and y2 = 4 Lesson 1-3: Formulas

  5. The slope m of a line containing two points with coordinates and is given by the formula where . Slope Formula Definition: In a coordinate plane, the slope of a line is the ratio of its vertical rise over its horizontal run. Formula: Example: Find the slope between (-2, -1) and (4, 5). Lesson 1-3: Formulas

  6. Describing Lines • Lines 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: Formulas

  7. m = m = Some More Examples • Find the slope between (4, -5) and (3, -5) and describe it. Since the slope is zero, the line must be horizontal. • Find the slope between (3,4) and (3,-2) and describe the line. Since the slope is undefined, the line must be vertical. Lesson 1-3: Formulas

  8. Example 3 : Find the slope of the line through the given points and describe the line. (7, 6) and (– 4, 6) left 11 (-11) y Solution: up 0 m (– 4, 6) (7, 6) x This line is horizontal. Lesson 1-3: Formulas

  9. Example 4:Find the slope of the line through the given points and describe the line. (– 3, – 2) and (– 3, 8) right 0 y Solution: (– 3, 8) m up 10 x (– 3, – 2) undefined This line is vertical. Lesson 1-3: Formulas

  10. Practice • Find 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

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