Review Centers - Washington County Schools

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1-Distance and Midpoint
Midpoint Formula
𝑀=(
π‘₯1 +π‘₯2 𝑦1 +𝑦2
2
,
2
)
Distance Formula
𝑑 = √(π‘₯2 βˆ’ π‘₯1 )2 + (𝑦2 βˆ’ 𝑦1 )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
𝑅𝑖𝑠𝑒
𝑅𝑒𝑛
Slope Formula
𝑦 βˆ’π‘¦
π‘š = π‘₯2 βˆ’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
𝑦 βˆ’ 𝑦1 = π‘š(π‘₯ βˆ’ π‘₯1 )
Slope-Intercept Form
𝑦 = π‘šπ‘₯ + 𝑏
Examples:
7
Point-Slope: m = βˆ’ 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 = βˆ’ 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:
⃑ are parallel, perpendicular or neither.
Determine if ⃑𝐴𝐡 and 𝐢𝐷
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 = βˆ’ 2x – 10
3
2.
⃑ are parallel, perpendicular or neither.
3. Determine if ⃑𝐴𝐡 and 𝐢𝐷
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=βˆ’ 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 = βˆ’ 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 = # β†’ horizontal line
* x = # β†’ vertical line
Examples:
1
2
y = 2x – 7
y = βˆ’ 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 β†’ CONGRUENT β†’ SET EQUAL
Alternate Interior β†’ CONGRUENT β†’ SET EQUAL
Alternate Exterior β†’ CONGRUENT β†’ SET EQUAL
Same Side Interior β†’ SUPPLEMENTARY β†’ ADD TO 180°
Examples:
Try These!
1.
2.
3.
4.
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