Final answer:
None of the triangle types listed—Right, Isosceles, Equilateral, or Scalene—could have vertices that fall on the same line as the two given points because that would contradict the definition of a triangle itself.
Step-by-step explanation:
The question asks which type of triangle could have vertices that lie on the same line as two given points, (0,18) and (-6,14). A triangle that has two or more vertices on the same line can not form a proper geometric figure as all vertices of a triangle should form three distinct points that are not collinear. This means that options a) Right triangle, b) Isosceles triangle, and c) Equilateral triangle are incorrect because none of these triangles can have vertices on the same line without violating their defining properties.
An isosceles triangle has two sides of equal length, an equilateral triangle has all sides of equal length, and a right triangle has one angle measuring 90 degrees. For all these triangles, the vertices must form a closed shape that does not align on a single line. The only option left is d) Scalene triangle, where all sides are of different lengths, but this also cannot lie on the same line as it would not meet the definition of a triangle.
None of the given options are valid; thus, the correct response should indicate that no such triangle can have its vertices on the same line as the two points provided.