Worksheet: Equations of Parallel and Perpendicular Lines

In this worksheet, we will practice creating the equations of parallel and perpendicular lines.

Q1:

Determine, in slope-intercept form, the equation of the line passing through 𝐴 ( 1 3 , 7 ) perpendicular to the line passing through 𝐵 ( 8 , 9 ) and 𝐶 ( 8 , 1 0 ) .

  • A 𝑦 = 1 9 1 6 𝑥 + 1 3 5 1 6
  • B 𝑦 = 1 6 1 9 𝑥 + 3 4 1 1 9
  • C 𝑦 = 1 9 1 6 𝑥 1 3 5 1 6
  • D 𝑦 = 1 6 1 9 𝑥 3 4 1 1 9
  • E 𝑦 = 3 4 1 1 9 𝑥 + 1 6 1 9

Q2:

If a line 𝐿 is perpendicular to the line 2 𝑦 + 1 0 = 6 𝑥 + 7 , and 𝐿 passes through the points 𝐴 ( 𝑛 , 1 0 ) and 𝐵 ( 7 , 2 ) , what is the value of 𝑛 ?

Q3:

Given that the coordinates of the points 𝐴 , 𝐵 , 𝐶 , and 𝐷 are ( 1 5 , 8 ) , ( 6 , 1 0 ) , ( 8 , 7 ) , and ( 6 , 1 6 ) , respectively, determine whether 𝐴 𝐵 and 𝐶 𝐷 are parallel, perpendicular, or neither.

  • Aneither
  • Bparallel
  • Cperpendicular

Q4:

Determine whether the lines 𝑦 = 1 7 𝑥 5 and 𝑦 = 1 7 𝑥 1 are parallel, perpendicular, or neither.

  • Aneither
  • Bperpendicular
  • Cparallel

Q5:

Find the slope of the line 2 𝑥 + 3 𝑦 2 = 0 and the 𝑦 -intercept of this line.

  • A 2 3 , 1
  • B 3 2 , 3 2
  • C 2 3 , 3 2
  • D 2 3 , 2 3

Q6:

If the slope of the straight line ( 3 𝑎 + 7 ) 𝑥 + 4 𝑎 𝑦 + 4 = 0 equals 1 , find the value of 𝑎 .

Q7:

Write, in the form 𝑦 = 𝑚 𝑥 + 𝑐 , the equation of the line that is parallel to the line 4 𝑥 + 7 𝑦 4 = 0 and that intercepts the 𝑦 -axis at 1.

  • A 𝑦 = 4 𝑥 + 1
  • B 𝑦 = 7 4 𝑥 + 1
  • C 𝑦 = 4 7 𝑥
  • D 𝑦 = 4 7 𝑥 + 1
  • E 𝑦 = 𝑥 4

Q8:

If 𝐴 ( 3 , 1 ) and 𝐵 ( 4 , 8 ) , find the cartesian equation of the straight line passing through the point of division of 𝐴 𝐵 internally in the ratio 4 3 and perpendicular to the straight line whose equation is 1 0 𝑥 + 3 𝑦 6 5 = 0 .

  • A 1 0 𝑥 + 3 𝑦 + 2 5 = 0
  • B 1 3 𝑥 + 1 0 𝑦 + 6 3 = 0
  • C 3 𝑥 + 1 0 𝑦 + 4 7 = 0
  • D 3 𝑥 1 0 𝑦 4 7 = 0

Q9:

Suppose that 𝐿 is the line 𝑎 𝑥 𝑦 + 1 5 = 0 , and 𝐿 the line 2 𝑥 3 + 𝑦 2 = 2 3 . Find the value of 𝑎 so that 𝐿 𝐿 .

  • A 2 3
  • B 3 4
  • C 1 3
  • D 4 3

Q10:

Lines 𝐴 and 𝐵 are perpendicular to each other and meet at ( 1 , 4 ) . If the slope of 𝐴 is 0, what is the equation of line 𝐵 ?

  • A 𝑥 = 4
  • B 𝑦 = 1
  • C 𝑦 = 4
  • D 𝑥 = 1
  • E 𝑦 = 0

Q11:

Given that the points 𝐴 ( 1 2 , 1 0 ) and 𝐵 ( 𝑥 , 8 ) lie on a line that has a slope of 1, determine the value of 𝑥 .

Q12:

Suppose that the points 𝐴 ( 3 , 1 ) , 𝐵 ( 1 , 2 ) , and 𝐶 ( 7 , 𝑦 ) form a right-angled triangle at 𝐵 . What is the value of 𝑦 ?

  • A 1 6
  • B 1 3 2
  • C 2
  • D 6

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