IM1H: 6.1Leaping Lizards

What do you want to remember about translations (#1), rotations (#2) and reflections (#3)

Consider the points A (2,3) and B (4,7) and the line segment AB between them. What is the slope of this line segment?

Locate a third point C(x,y) on the coordinate grid, so that the points A(2,3), B(4,7), and C(x,y) form the vertices of a right triangle with AB as its hypotenuse. Explain how you know that the triangle you formed contains a right triangle.

Now rotate this triangle 90 degrees counter clockwise about the vertex point (2,3). Explain how you know that you have rotated the triangle 90 degrees. (draw a new triangle in the applet above).

Compare the slope of the hypotenuse of this rotated right triangle with the slope of the hypotenuse of the pre-image. What do you notice?

What is the slope of AB?

Locate a third point C(x,y) on the coordinate grid, so that the points A(2,3), B(5,4), and C(x,y) form the vertices of a right triangle with AB as its hypotenuse. Explain how you know that the triangle you formed contains a right triangle?

Now rotate this triangle 90 degrees counter clockwise about the vertex point (2,3). Explain how you know that you have rotated the triangle 90 degrees. (draw a new triangle in the applet above).

Compare the slope of the hypotenuse of this rotated right triangle with the slope of the hypotenuse of the pre-image. What do you notice?

What do you notice about perpendicular lines from this activity? (List as many things as you can).