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

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:

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

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

Q2:

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)

Q3:

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

Q4:

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)

Q5:

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

Q6:

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

Q7:

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)

Q8:

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

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:

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

This lesson includes 18 additional questions and 234 additional question variations for subscribers.

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