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Worksheet: Slope: Parallel & Perpendicular Lines

Q1:

Two lines and have gradients of and respectively. Are the two lines parallel?

  • ANo
  • BYes

Q2:

Two lines have slopes of 6 5 and 1 2 1 0 . Are the two lines parallel?

  • AYes
  • BNo

Q3:

Two lines and have gradients of and respectively. Are the two lines perpendicular?

  • AYes
  • BNo

Q4:

Describe the relative positions of the straight lines 2 π‘₯ = 3 and 5 𝑦 = 8 .

  • AThey are parallel.
  • BThey are coincident.
  • CThey are perpendicular.

Q5:

How would you describe the relation between the lines 𝑦 = 1 7 π‘₯ + 9 and βˆ’ π‘₯ + 7 𝑦 + 4 = 0 ?

  • Aperpendicular
  • Bcoincident
  • Cintersecting and not perpendicular
  • Dparallel

Q6:

Let 𝐿 be the line through the points ( βˆ’ 7 , βˆ’ 7 ) and ( βˆ’ 9 , 6 ) and 𝑀 the line through ( 1 , 1 ) and ( 1 4 , 3 ) . Which of the following is true about the lines 𝐿 and 𝑀 ?

  • AThey are intersecting but not perpendicular.
  • BThey are parallel.
  • CThey are perpendicular.

Q7:

The line 𝐿 1 passes through the points ( 3 , 3 ) and ( βˆ’ 1 , 0 ) , and the line 𝐿 2 passes through the points ( βˆ’ 3 , 2 ) and ( 0 , βˆ’ 2 ) . Are the two lines perpendicular?

  • A yes
  • B no

Q8:

What is the value of 𝑏 , if lines βˆ’ 2 π‘₯ + 𝑏 𝑦 + 6 = 0 and βˆ’ π‘₯ βˆ’ 4 𝑦 βˆ’ 3 = 0 are parallel?

  • A βˆ’ 4
  • B 1 2
  • C βˆ’ 2
  • D βˆ’ 8

Q9:

The line through points ( 5 , 7 ) and ( 1 , 𝑝 ) is parallel to the line 𝑝 βˆ’ 3 π‘₯ βˆ’ 7 = 0 . Find 𝑝 .

Q10:

If the line that passes through the points 𝐴 ( 6 , 0 ) and 𝐡 ( 4 , βˆ’ 6 ) is perpendicular to the line passing through the points 𝐢 ( βˆ’ 9 , 1 9 ) and 𝐷 ( π‘₯ , 1 5 ) , what is the value of π‘₯ ?

Q11:

The line on the points ( 1 0 , π‘˜ + 2 ) and 𝐡 ( 7 , 1 0 ) is parallel to one that makes an angle of 1 0 0 ∘ with the positive π‘₯ -axis. Determine π‘˜ to the nearest integer.

  • A11
  • B7
  • C9
  • D βˆ’ 9

Q12:

Describe the relative positions of the straight lines 4 π‘₯ βˆ’ 4 𝑦 = 5 and 3 2 π‘₯ βˆ’ 3 2 𝑦 = 4 0 .

  • AThey are perpendicular.
  • BThey are parallel.
  • CThey are coincident.

Q13:

How would you describe the relation between the lines 𝑦 = π‘₯ βˆ’ 9 and βˆ’ π‘₯ + 𝑦 βˆ’ 4 = 0 ?

  • Aperpendicular
  • Bcoincident
  • Cintersecting and not perpendicular
  • Dparallel

Q14:

How would you describe the relation between the lines 𝑦 = βˆ’ 7 2 π‘₯ βˆ’ 2 and 7 π‘₯ + 2 𝑦 + 4 = 0 ?

  • Aperpendicular
  • Bparallel
  • Cintersecting and not perpendicular
  • Dcoincident

Q15:

How would you describe the relation between the lines 𝑦 = βˆ’ 4 π‘₯ βˆ’ 1 2 and 8 π‘₯ + 2 𝑦 + 1 = 0 ?

  • Aperpendicular
  • Bparallel
  • Cintersecting and not perpendicular
  • Dcoincident

Q16:

What is the value of 𝑏 , if lines 5 π‘₯ + 𝑏 𝑦 βˆ’ 2 = 0 and βˆ’ 4 π‘₯ βˆ’ 5 𝑦 + 1 = 0 are parallel?

  • A βˆ’ 5
  • B βˆ’ 4
  • C βˆ’ 2
  • D 2 5 4

Q17:

Let 𝐿 be the line through the points ( βˆ’ 4 , 9 ) and ( 0 , βˆ’ 5 ) and 𝑀 the line through ( βˆ’ 1 2 , 1 7 ) and ( βˆ’ 2 6 , 1 3 ) . Which of the following is true about the lines 𝐿 and 𝑀 ?

  • AThey are intersecting but not perpendicular.
  • BThey are parallel.
  • CThey are perpendicular.

Q18:

Let 𝐿 be the line through the points ( βˆ’ 7 , 6 ) and ( βˆ’ 2 , 1 ) and 𝑀 the line through ( βˆ’ 1 2 , 4 ) and ( βˆ’ 7 , βˆ’ 1 ) . Which of the following is true about the lines 𝐿 and 𝑀 ?

  • AThey are intersecting but not perpendicular.
  • BThey are perpendicular.
  • CThey are parallel.

Q19:

The line through points ( βˆ’ 7 , 0 ) and ( βˆ’ 2 , 𝑝 ) is perpendicular to the line βˆ’ 8 𝑝 βˆ’ 4 π‘₯ + 9 = 0 . Find 𝑝 .

Q20:

The line through points ( βˆ’ 1 , βˆ’ 9 ) and ( βˆ’ 4 , 𝑝 ) is perpendicular to the line 8 𝑝 βˆ’ π‘₯ βˆ’ 6 = 0 . Find 𝑝 .