Alignment to Content Standards:

CCSS.MATH.CONTENT.HSG.GPE.B.4

Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

CCSS.MATH.CONTENT.HSG.GPE.B.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Tasks

Plot these points on an x/y coordinate plane: A(4, 0), B(0, 3), C(-3, -1), and D(1, -4)

1) Find the length of segment AB.

 

2) Find the slope of segments AB and CB.

 

3) Join the sides of quadrilateral ABCD. Prove that quadrilateral ABCD is a square. How do the answers in question 2 aid in this proof?

 

For the full commentary and solution to the task, open the following attachment:

Assessment Item