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Worksheet: Equations of Parallel and Perpendicular Lines

Q1:

Suppose that the points , , and form a right triangle at . What is the value of ?

  • A
  • B
  • C
  • D

Q2:

Given that the coordinates of the points 𝐴 , 𝐡 , 𝐢 , and 𝐷 are ( βˆ’ 1 5 , 8 ) , ( βˆ’ 6 , 1 0 ) , ( βˆ’ 8 , βˆ’ 7 ) , and ( βˆ’ 6 , βˆ’ 1 6 ) , respectively, determine whether βƒ–     βƒ— 𝐴 𝐡 and βƒ–     βƒ— 𝐢 𝐷 are parallel, perpendicular, or neither.

  • Aneither
  • Bparallel
  • Cperpendicular

Q3:

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

  • A 𝑦 = βˆ’ 1 9 1 6 π‘₯ + 1 3 5 1 6
  • B 𝑦 = 1 6 1 9 π‘₯ + 3 4 1 1 9
  • C 𝑦 = βˆ’ 1 9 1 6 π‘₯ βˆ’ 1 3 5 1 6
  • D 𝑦 = 1 6 1 9 π‘₯ βˆ’ 3 4 1 1 9
  • E 𝑦 = βˆ’ 3 4 1 1 9 π‘₯ + 1 6 1 9

Q4:

Write, in the form 𝑦 = π‘š π‘₯ + 𝑐 , the equation of the line that is parallel to the line βˆ’ 4 π‘₯ + 7 𝑦 βˆ’ 4 = 0 and that intercepts the 𝑦 -axis at 1.

  • A 𝑦 = βˆ’ 4 π‘₯ + 1
  • B 𝑦 = βˆ’ 7 4 π‘₯ + 1
  • C 𝑦 = 4 7 π‘₯
  • D 𝑦 = 4 7 π‘₯ + 1
  • E 𝑦 = π‘₯ βˆ’ 4

Q5:

If 𝐴 ( 3 , βˆ’ 1 ) and 𝐡 ( βˆ’ 4 , βˆ’ 8 ) , find the cartesian equation of the straight line passing through the point of division of 𝐴 𝐡 internally in the ratio 4 ∢ 3 and perpendicular to the straight line whose equation is 1 0 π‘₯ + 3 𝑦 βˆ’ 6 5 = 0 .

  • A 1 0 π‘₯ + 3 𝑦 + 2 5 = 0
  • B 1 3 π‘₯ + 1 0 𝑦 + 6 3 = 0
  • C 3 π‘₯ + 1 0 𝑦 + 4 7 = 0
  • D 3 π‘₯ βˆ’ 1 0 𝑦 βˆ’ 4 7 = 0

Q6:

If the gradient of the straight line equals , find the value of .

  • A1
  • B
  • C
  • D7

Q7:

Find the gradient of the line and the -intercept of this line.

  • A , 1
  • B ,
  • C ,
  • D ,

Q8:

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

  • A π‘₯ = 4
  • B 𝑦 = βˆ’ 1
  • C 𝑦 = 4
  • D π‘₯ = βˆ’ 1
  • E 𝑦 = 0

Q9:

Determine whether the lines 𝑦 = βˆ’ 1 7 π‘₯ βˆ’ 5 and 𝑦 = βˆ’ 1 7 π‘₯ βˆ’ 1 are parallel, perpendicular, or neither.

  • Aneither
  • Bperpendicular
  • Cparallel

Q10:

Given that the points 𝐴 ( 1 2 , 1 0 ) and 𝐡 ( π‘₯ , βˆ’ 8 ) lie on a line that has a slope of 1, determine the value of π‘₯ .

Q11:

If a line 𝐿 is perpendicular to the line βˆ’ 2 𝑦 + 1 0 = βˆ’ 6 π‘₯ + 7 , and 𝐿 passes through the points 𝐴 ( 𝑛 , βˆ’ 1 0 ) and 𝐡 ( βˆ’ 7 , 2 ) , what is the value of 𝑛 ?

Q12:

Suppose that is the line , and the line . Find the value of so that .

  • A
  • B
  • C
  • D