Month: August 2018

The following lines on a cartesian plane make the outline of a shape:

(0,4) to (3,3)
(3,3) to (4,0)
(4.0) to (3,-3)
(3,-3) to (0,-4)
(0,-4) to (-3,-3)
(-3,-3) to (-4,0)
(-4,0) to (-3,3)
(-3,3) to (0,4)

1) Find the gradient of each line.

2) Find the y intercept if not known

3) Find the length of each line. (Are all the lengths the same? Shortcuts are allowed.)

4) Which lines are parallel and which are perpendicular

5) For each line, find the midpoint and find the equation for the line that is perpendicular.

6) For each of the perpendicular lines found, identify the y intercept.

7) What type of shape is outlined by the original lines?

Stretch question:

Is this the ‘regular’ version of the shape? If not, what would be required to convert it to the regular version.

Try expanding these binomials, (Don’t use an air pump or they will explode and turn into power series – jk 😉 Instead use FOIL – First, Outside, Inside, Last)

There is something interesting about the last four expansions. What do they have in common and how can you spot it without expanding the expression?