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Lesson: Vertices of Isosceles Triangles on the Coordinate Plane

Sample Question Videos

Worksheet • 4 Questions • 2 Videos

Q1:

Give the coordinates of the vertices 𝐴 and 𝐢 .

  • A 𝐴 ( π‘Ž , π‘Ž ) , 𝐢 ( 0 , π‘Ž )
  • B 𝐴 ( π‘Ž , π‘Ž ) , 𝐢 ( π‘Ž , 0 )
  • C 𝐴 ( π‘Ž , π‘Ž ) , 𝐢 ( π‘Ž , π‘Ž )
  • D 𝐴 ( 0 , π‘Ž ) , 𝐢 ( π‘Ž , π‘Ž )

Q2:

A triangle 𝑂 𝐴 𝐡 is drawn in the first quadrant with one vertex at 𝑂 ( 0 , 0 ) . Vertex 𝐴 is on the π‘₯ -axis and the midpoint of 𝑂 𝐡 is ο€» π‘Ž 3 , π‘Ž  . The height of the triangle is equal to the length of its base 𝑂 𝐴 .

State the coordinates of vertices 𝐴 and 𝐡 .

  • A 𝐴 ( 2 π‘Ž , 0 ) , 𝐡 ο€Ό 2 π‘Ž 3 , 2 π‘Ž 
  • B 𝐴 ( 2 π‘Ž , 0 ) , 𝐡 ο€» π‘Ž 3 , 2 π‘Ž 
  • C 𝐴 ( 2 π‘Ž , 0 ) , 𝐡 ο€» βˆ’ π‘Ž 3 , 2 π‘Ž 
  • D 𝐴 ( 4 π‘Ž , 0 ) , 𝐡 ο€» βˆ’ π‘Ž 3 , 4 π‘Ž 
  • E 𝐴 ( 4 π‘Ž , 0 ) , 𝐡 ο€Ό 2 π‘Ž 3 , 4 π‘Ž 

Q3:

Give the coordinates of the vertices 𝐴 , 𝐡 , and 𝐢 .

  • A 𝐴 ( 0 , 𝑏 ) , 𝐡 ( π‘Ž , 0 ) , 𝐢 ( βˆ’ π‘Ž , 0 )
  • B 𝐴 ( 0 , 𝑏 ) , 𝐡 ( π‘Ž , 𝑏 ) , 𝐢 ( βˆ’ π‘Ž , 𝑏 )
  • C 𝐴 ( 0 , 𝑏 ) , 𝐡 ( π‘Ž , 0 ) , 𝐢 ( βˆ’ π‘Ž , βˆ’ 𝑏 )
  • D 𝐴 ( π‘Ž , 𝑏 ) , 𝐡 ( π‘Ž , 0 ) , 𝐢 ( βˆ’ π‘Ž , 0 )
  • E 𝐴 ( 0 , 𝑏 ) , 𝐡 ( π‘Ž , 𝑏 ) , 𝐢 ( βˆ’ π‘Ž , 0 )

Q4:

Give the coordinates of the vertices 𝐡 and 𝐢 .

  • A 𝐡 ( 2 π‘Ž , 0 ) , 𝐢 ( 0 , 0 )
  • B 𝐡 ( 2 𝑏 , 0 ) , 𝐢 ( 2 π‘Ž , 2 𝑏 )
  • C 𝐡 ( 2 𝑏 , 0 ) , 𝐢 ( 0 , 0 )
  • D 𝐡 ( 0 , 2 𝑏 ) , 𝐢 ( 0 , 0 )
  • E 𝐡 ( 0 , 2 π‘Ž ) , 𝐢 ( 0 , 0 )
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