Overview:  On the second page of the problem, Jaipal uses tracing paper to make a copy of the front tree on the other side of the street.  Patrick is working on making the 2-story house, and he doubled the height of the house to make it 2 stories.  After doubling the height, Patrick tries to copy the roof from the front house onto the back house.  Olive constructs what she calls a vanishing point (though it’s not the correct vanishing point) by drawing a line segment between the front two houses and then constructing the perpendicular bisector of that segment.  Then, Olive draws another line segment from the front tree to the perpendicular bisector, and she labels the intersection the vanishing point.  Olive tells the other students in the group that everything in the picture should line up with the vanishing point that she has drawn.

Prior knowledge:   On the second page of the problem, Jaipal uses school mathematics knowledge of scale factor to double the height of the house, although he does not apply the concept of scale factor to the roof of the house.  Olive uses a novel mathematical practice to construct the vanishing point of the diagram.  Olive is correct that the vanishing point of the picture would lie on the perpendicular bisector she has constructed, but Olive arbitrarily selects a point along that segment.  The point Olive names as the vanishing point is not the vanishing point that already exists in the diagram.

Other points of interest:  Olive’s work, especially on the second page of the problem, illustrates the historical evolution of the concept of vanishing point in works of art.  When artists first began to use perspective in their work in the 15th century, they often identified multiple, contradictory vanishing points in a single drawing.  In Olive’s work we can see that she is using the idea of a vanishing point, but the point she identifies is different than the vanishing point that already exists in the drawing.