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Common Core Standard HSG-GPE.B.5 Questions

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

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Grade 9 Coordinate Geometry CCSS: HSG-GPE.B.5
Line q contains points (0,0) and (-5,5). What is the distance between line q and the point P(1,5)?
  1. [math]sqrt(6)[/math]
  2. [math]4[/math]
  3. [math]sqrt(18)[/math]
  4. [math]6.5[/math]
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Write an equation in slope-intercept form that is perpendicular to the equation y = -2x + 3 and passes through the point (4,2).
  1. [math] y = -2x + 2 [/math]
  2. [math]y = 1/2 x + 2[/math]
  3. [math] y = -2x + 10 [/math]
  4. [math]y = 1/2x[/math]
Grade 9 Coordinate Geometry CCSS: HSG-GPE.B.5
Find the distance between the parallel lines r and s whose equations are y = -3x - 5 and y = -3x + 6.
  1. [math]sqrt(23)[/math]
  2. [math]6[/math]
  3. [math]sqrt(18)[/math]
  4. [math]sqrt(12.1)[/math]
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Choose the equation of a line that is perpendicular to [math]3x+4y=2[/math] and passes through (3, 1).
  1. [math]y = -3/4 x + 13/4[/math]
  2. [math]y = -4/3 x +5[/math]
  3. [math]y = 3/4 x - 5/4[/math]
  4. [math]y = 4/3 x -3[/math]
Grade 9 Coordinate Geometry CCSS: HSG-GPE.B.5
Which of the following is the equation of a line that is perpendicular to y = -2x - 3 and passes through the point (-3, 3)?
  1. [math]y=2x+4[/math]
  2. [math]y=-2x+ 9/4[/math]
  3. [math]y=1/2x+ 9/2[/math]
  4. [math]y=-1/2x+ 9/4[/math]
Grade 10 Linear Equations CCSS: HSG-GPE.B.5
Write the equation of a line parallel to [math]y=2/5 x-3[/math] that goes through the point (1,-1).
  1. [math]y=5/2x-3[/math]
  2. [math]y=2/5x-7/5[/math]
  3. [math]y=-5/2x-7/5[/math]
  4. [math]y=-5/2x+3/2[/math]
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Write the equation of the line in slope-intercept form passing through the point (-6, 7) and parallel to [math]3x + 7y = 3.[/math]
  1. [math]y = 3/7x - 31/7[/math]
  2. [math]y = -7/3x + 7/3[/math]
  3. [math]y = -3/7x + 31/7[/math]
  4. [math]y = 3/7x + 3/7[/math]
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Write the equation of the line in slope-intercept form passing through the point (-5, -2) and perpendicular to [math]-5x - 2y = 27.[/math]
  1. [math]y = 5/2x + 21/2[/math]
  2. [math]y = 2/5x[/math]
  3. [math]y = -5/2x - 29/2[/math]
  4. [math]y - -2/5x - 4[/math]
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Choose the equation of a line passing through (3, 1) that is perpendicular to [math]y=(-1/2)x-(1/4)[/math].
  1. [math]y=2x-5[/math]
  2. [math]y=3x-1[/math]
  3. [math]y=(1/2)x-6[/math]
  4. [math]y=(1/2)x+(1/2)[/math]
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Which equation passes through [math](-1,1)[/math] and is parallel to [math]y=-2x+1[/math]?
  1. [math]y=-2x-1[/math]
  2. [math]y=1/2x+1/3[/math]
  3. [math]y=-2x+1[/math]
  4. [math]y=-1/2x-1/2[/math]
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