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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. $sqrt(6)$
2. $4$
3. $sqrt(18)$
4. $6.5$
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. $y = -2x + 2$
2. $y = 1/2 x + 2$
3. $y = -2x + 10$
4. $y = 1/2x$
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. $sqrt(23)$
2. $6$
3. $sqrt(18)$
4. $sqrt(12.1)$
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Choose the equation of a line that is perpendicular to $3x+4y=2$ and passes through (3, 1).
1. $y = -3/4 x + 13/4$
2. $y = -4/3 x +5$
3. $y = 3/4 x - 5/4$
4. $y = 4/3 x -3$
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
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. $y=2x+4$
2. $y=-2x+ 9/4$
3. $y=1/2x+ 9/2$
4. $y=-1/2x+ 9/4$
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Grade 10 Linear Equations CCSS: HSG-GPE.B.5
Write the equation of a line parallel to $y=2/5 x-3$ that goes through the point (1,-1).
1. $y=5/2x-3$
2. $y=2/5x-7/5$
3. $y=-5/2x-7/5$
4. $y=-5/2x+3/2$
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
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 $3x + 7y = 3.$
1. $y = 3/7x - 31/7$
2. $y = -7/3x + 7/3$
3. $y = -3/7x + 31/7$
4. $y = 3/7x + 3/7$
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
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 $-5x - 2y = 27.$
1. $y = 5/2x + 21/2$
2. $y = 2/5x$
3. $y = -5/2x - 29/2$
4. $y - -2/5x - 4$
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Choose the equation of a line passing through (3, 1) that is perpendicular to $y=(-1/2)x-(1/4)$.
1. $y=2x-5$
2. $y=3x-1$
3. $y=(1/2)x-6$
4. $y=(1/2)x+(1/2)$
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Which equation passes through $(-1,1)$ and is parallel to $y=-2x+1$?
1. $y=-2x-1$
2. $y=1/2x+1/3$
3. $y=-2x+1$
4. $y=-1/2x-1/2$
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
Grade 9 Linear Equations CCSS: HSG-GPE.B.5
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