Worksheet: Vertices of Isosceles Triangles on the Coordinate Plane

In this worksheet, we will practice deducing the coordinates of a vertex of an isosceles triangle on a coordinate plane.

Q1:

Give the coordinates of the vertices 𝐴 and 𝐶 .

  • A 𝐴 ( 0 , 𝑎 ) , 𝐶 ( 𝑎 , 𝑎 )
  • B 𝐴 ( 𝑎 , 𝑎 ) , 𝐶 ( 𝑎 , 0 )
  • C 𝐴 ( 𝑎 , 𝑎 ) , 𝐶 ( 𝑎 , 𝑎 )
  • D 𝐴 ( 𝑎 , 𝑎 ) , 𝐶 ( 0 , 𝑎 )

Q2:

Give the coordinates of the vertices 𝐴 , 𝐵 , and 𝐶 .

  • A 𝐴 ( 0 , 𝑏 ) , 𝐵 ( 𝑎 , 𝑏 ) , 𝐶 ( 𝑎 , 0 )
  • B 𝐴 ( 0 , 𝑏 ) , 𝐵 ( 𝑎 , 0 ) , 𝐶 ( 𝑎 , 𝑏 )
  • C 𝐴 ( 𝑎 , 𝑏 ) , 𝐵 ( 𝑎 , 0 ) , 𝐶 ( 𝑎 , 0 )
  • D 𝐴 ( 0 , 𝑏 ) , 𝐵 ( 𝑎 , 0 ) , 𝐶 ( 𝑎 , 0 )
  • E 𝐴 ( 0 , 𝑏 ) , 𝐵 ( 𝑎 , 𝑏 ) , 𝐶 ( 𝑎 , 𝑏 )

Q3:

Give the coordinates of the vertices 𝐵 and 𝐶 .

  • A 𝐵 ( 0 , 2 𝑎 ) , 𝐶 ( 0 , 0 )
  • B 𝐵 ( 2 𝑏 , 0 ) , 𝐶 ( 0 , 0 )
  • C 𝐵 ( 0 , 2 𝑏 ) , 𝐶 ( 0 , 0 )
  • D 𝐵 ( 2 𝑎 , 0 ) , 𝐶 ( 0 , 0 )
  • E 𝐵 ( 2 𝑏 , 0 ) , 𝐶 ( 2 𝑎 , 2 𝑏 )

Q4:

A triangle 𝑂 𝐴 𝐵 is drawn in the first quadrant with one vertex at 𝑂 ( 0 , 0 ) . Vertex 𝐴 is on the 𝑥 -axis and the midpoint of 𝑂 𝐵 is 𝑎 3 , 𝑎 . The height of the triangle is equal to the length of its base 𝑂 𝐴 .

State the coordinates of vertices 𝐴 and 𝐵 .

  • A 𝐴 ( 4 𝑎 , 0 ) , 𝐵 2 𝑎 3 , 4 𝑎
  • B 𝐴 ( 2 𝑎 , 0 ) , 𝐵 𝑎 3 , 2 𝑎
  • C 𝐴 ( 4 𝑎 , 0 ) , 𝐵 𝑎 3 , 4 𝑎
  • D 𝐴 ( 2 𝑎 , 0 ) , 𝐵 2 𝑎 3 , 2 𝑎
  • E 𝐴 ( 2 𝑎 , 0 ) , 𝐵 𝑎 3 , 2 𝑎

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.