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1-Distance and Midpoint Midpoint Formula π=( π₯1 +π₯2 π¦1 +π¦2 2 , 2 ) Distance Formula π = √(π₯2 − π₯1 )2 + (π¦2 − π¦1 )2 Example: Find the midpoint and distance between (-6, 2) and (4, -1). Try These! Find the distance and midpoint. Round to the nearest hundredth. 1. (-1, 8) (-7, -3) 2. (0, -5) (4, -9) 2-Slope Graphs π ππ π π π’π Slope Formula π¦ −π¦ π = π₯2 −π₯1 2 1 Examples: (-5, -1) (6, -3) Try These! 1. 4. (-1, 7) (-6, 7) 2. 3. 5. (-4, -9) (-8, 5) 3-Equations of Lines Point-Slope Form π¦ − π¦1 = π(π₯ − π₯1 ) Slope-Intercept Form π¦ = ππ₯ + π Examples: 7 Point-Slope: m = − 4 (8, -4) Slope-Intercept: m = 2 Try These! Write in point-slope form. 1. m = -2 (-8, 4) 2. m = 5 (-3, 1) Write in slope-intercept form. 3. m = 7 (-2, 9) 4. m = − 4 1 3 3 (-12, -3) (6, -1) 4-Slopes of Parallel & Perpendicular Lines Parallel Lines→ same slope Perpendicular Lines→ slopes are opposite reciprocals (change sign & flip) Examples: β‘ are parallel, perpendicular or neither. Determine if β‘π΄π΅ and πΆπ· A(5, 7) B(3, 4) C(-1, 6) D(2, 8) 5 y =3 x + 8 y = 5x + 10 y = 4x – 8 2 Try These! 1. 4 y = − 2x – 10 3 2. β‘ are parallel, perpendicular or neither. 3. Determine if β‘π΄π΅ and πΆπ· A(-1, 5) B(0, 8) C(-9, -7) D(-11, -13) 4. y = 2x + 7 4 y= x+1 2 5 5. y = x + 4 9 9 y=− x–6 5 5-Equations of Parallel & Perpendicular Lines 1) Get slope from original equation. 2) Plug slope and point into point-slope form. 3) Distribute and solve for y to get into slope-intercept. Examples: Write the slope-intercept form of an equation for the line that passes through (-7, 4) and is parallel to the graph of y = 9x – 5. Write the slope-intercept form of an equation for the line that passes through (8, -2) and is perpendicular to the graph of y = -2x + 3. Try These! 1. Write the slope-intercept form of an equation for the line that passes 1 through (9, -1) and is parallel to the graph of y = 3x – 15. 2. Write the slope-intercept form of an equation for the line that passes 1 through (-4, -3) and is perpendicular to the graph of y = − 2x – 8. 6-Graphing Lines y = mx + b 1) Plot y-intercept(b) on y-axis 2) Use slope(m) to rise and run * y = # → horizontal line * x = # → vertical line Examples: 1 2 y = 2x – 7 y = − 3x + 4 y=6 Try these! 1 1. y = 3x -2 3. x = 4 2. y = -x + 9 7-Lines and Transversals Corresponding: Alternate Interior: Alternate Exterior: Same Side Interior: Examples: Name the relationship between x and y. Try These! Name the relationship between x and y. 1. 2. 4. 5. 3. 8-Parallel Lines and Transversals Corresponding → CONGRUENT → SET EQUAL Alternate Interior → CONGRUENT → SET EQUAL Alternate Exterior → CONGRUENT → SET EQUAL Same Side Interior → SUPPLEMENTARY → ADD TO 180° Examples: Try These! 1. 2. 3. 4.