Worksheet: Intersection Point of Two Straight Lines on the Coordinate Plane

In this worksheet, we will practice finding the intersection point between two straight lines on a coordinate system and using this concept to find equations of lines.

Q1:

Find the equation of the line perpendicular to 6𝑥𝑦+8=0 and passing through the intersection of the lines 4𝑥𝑦3=0 and 3𝑥+8𝑦1=0.

  • A173𝑥158𝑦+101=0
  • B2𝑥3𝑦+1=0
  • C7𝑥42𝑦1=0
  • D19𝑥39𝑦+8=0

Q2:

Determine the equation of the line passing through the point of intersection of the two lines whose equations are 5𝑥+2𝑦=0 and 3𝑥+7𝑦+13=0 while making an angle of 135 with the positive 𝑦-axis.

  • A29𝑥+𝑦91=0
  • B29𝑥29𝑦91=0
  • C29𝑥+29𝑦39=0
  • D29𝑥+29𝑦+39=0

Q3:

Find the equation of the straight line that passes through the origin and the point of intersection of the two straight lines 𝑥=174 and 𝑦=5.

  • A𝑦=2017𝑥
  • B𝑦=854𝑥
  • C𝑦=2017𝑥
  • D𝑦=1720𝑥

Q4:

Find the equation of the straight line that is parallel to the 𝑦-axis and passes through the point of intersection of the two straight lines 𝑦=3 and 𝑥=1115𝑦.

  • A𝑦=115
  • B𝑥=115
  • C𝑥=115
  • D𝑥=115𝑦

Q5:

What is the equation of the line passing through 𝐴(1,3) and the intersection of the lines 3𝑥𝑦+5=0 and 5𝑥+2𝑦+3=0?

  • A17𝑥2𝑦+23=0
  • B23𝑥+7𝑦+17=0
  • C8𝑥+𝑦+8=0

Q6:

Find the equation of the straight line that passes through the point of intersection of the two straight lines 𝑥8𝑦=2 and 6𝑥8𝑦=1 and is parallel to the 𝑦-axis.

  • A𝑥=17
  • B𝑥=17
  • C𝑥=1356
  • D𝑥=17𝑦

Q7:

Find the equation of the straight line which passes through the point of intersection of the two lines 13𝑥5𝑦=14 and 2𝑥+15𝑦=11 and is parallel to the straight line 𝑥+8𝑦=14.

  • A𝑦18𝑥=215296
  • B𝑦8𝑥+215296=0
  • C𝑦18𝑥=215296
  • D𝑦+18𝑥=215296

Q8:

Find the equation of the straight line which passes through the point of intersection of the two lines 4𝑥+15𝑦=15 and 4𝑥+3𝑦=14 and is parallel to the straight line r=4,0+𝑘5,4.

  • A𝑦+45𝑥=203
  • B𝑦54𝑥=203
  • C𝑦54𝑥=203
  • D𝑦45𝑥+203=0

Q9:

Find the vector equation of the straight line that is parallel to the 𝑦-axis and passes through the point of intersection of the two straight lines r=𝑘6,4 and 3𝑥+5𝑦=5.

  • Ar=1,0+𝑘15,10
  • Br=15,10+𝑘0,1
  • Cr=0,1+𝑘15,10
  • Dr=15,10+𝑘1,0

Q10:

Find the vector equation of the straight line that passes through the point of intersection of the two straight lines 8𝑥𝑦=7 and 5𝑥3𝑦=2 and the point (12,8).

  • Ar=(12,8)+𝑘(7,13)
  • Br=(12,8)+𝑘(13,7)
  • Cr=12,8+𝑘13,7
  • Dr=(13,7)+𝑘(12,8)

Q11:

Find the 𝑥-coordinate of the point at which the straight line 3𝑥+9𝑦=0 cuts the 𝑥-axis.

Q12:

The lines 𝑥+𝑦+4=0 and 𝑟=(1,4)+𝐾(2,2) intersect orthogonally. Find the coordinates of the point of intersection.

  • A(0,9)
  • B92,12
  • C(8,8)
  • D(2,3)

Q13:

Find the equation of the straight line that passes through the point of intersection of the two lines 5𝑥14𝑦=6 and 𝑥10𝑦=9, given that it is perpendicular to the second line.

  • A𝑦10𝑥+23312=0
  • B𝑦10𝑥=23312
  • C𝑦110𝑥=23312
  • D𝑦+10𝑥=23312

Q14:

Find the point of intersection of the two straight lines 11𝑥+20=0 and 11𝑦+2=0.

  • A(20,2)
  • B211,2011
  • C2011,211
  • D2011,211

Q15:

Find the equation of the straight line that passes through the point of intersection of the two straight lines 9𝑥+2𝑦=1 and 2𝑥𝑦=12 and intersects the negative direction of the 𝑦-axis at a point that is 10 length units away from the origin.

  • A𝑦+512𝑥=110
  • B𝑦125𝑥=110
  • C𝑦+125𝑥=10
  • D𝑦+125𝑥=10

Q16:

Determine the point of intersection of the two straight lines represented by the equations 𝑥+3𝑦2=0 and 𝑦+1=0.

  • A(1,1)
  • B(2,4)
  • C(1,1)
  • D(1,1)

Q17:

Find the equation of the straight line, passing through the point of intersection of the two straight lines 𝑦9=0 and 𝑥𝑦=0, that intersects the positive directions of the coordinate axes in two points at the same distance from the origin.

  • A𝑥+𝑦=0
  • B𝑥+𝑦18=0
  • C𝑥𝑦18=0
  • D𝑥+𝑦+18=0

Q18:

What is the equation of the line passing through 𝐴(3,5) and the intersection of the lines 4𝑥+2𝑦+1=0 and 2𝑥+3𝑦2=0?

  • A30𝑥+17𝑦+5=0
  • B18𝑥+23𝑦13=0
  • C6𝑥+5𝑦1=0

Q19:

Find the coordinates of the intersection point between a straight line represented by the equation 3𝑥9𝑦=9 and the 𝑦-axis.

  • A(0,1)
  • B(1,0)
  • C(0,1)
  • D
  • E(0,9)

Q20:

At which point do the lines 𝑥=7 and 16𝑦=1 intersect?

  • A(7,6)
  • B(7,6)
  • C(7,6)
  • D(7,6)

Q21:

Find the intersection point of the two straight lines r=𝐾3,5 and 𝑥+3𝑦=0.

  • A(3,1)
  • B(5,3)
  • C(0,0)
  • D(3,5)
  • E(1,3)

Q22:

Find the intersection of the lines 𝑥+13=7 and 𝑦16=0.

  • A(16,6)
  • B(6,16)
  • C(6,16)
  • D(20,16)
  • E(16,20)

Q23:

At which point do the lines 25𝑥=4 and 10𝑦=2 intersect?

  • A(20,10)
  • B(5,20)
  • C(10,5)
  • D(20,5)
  • E(5,10)

Q24:

Where do the straight lines 7𝑥+8𝑦=22 and 9𝑥4𝑦=14 intersect?

  • Athird quadrant
  • Bfirst quadrant
  • Csecond quadrant
  • Dfourth quadrant
  • Eorigin

Q25:

The coordinates of the points 𝐴 and 𝐵 are (5,8) and (8,4) respectively. Given that 𝐴𝐵 intersects the 𝑥-axis at 𝐶 and the 𝑦-axis at 𝐷, determine the coordinates of 𝐶 and 𝐷.

  • A𝐶(0,28), 𝐷(7,0)
  • B𝐶(6,0), 𝐷(0,24)
  • C𝐶(7,0), 𝐷(0,28)
  • D𝐶(0,7), 𝐷(28,0)

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