a. Consider the points [math]A(2,3)[/math] and [math]B(0,6)[/math] and the line segment,[math]\overline{AB}[/math] , between them. What is the slope of this line segment?
b. Drag the point [math]C[/math], on the coordinate grid, so that the points [math]A(2,3)[/math], [math]B\left(0,6\right)[/math], and [math]C(x,y)[/math] form the vertices of a right triangle, with [math]\overline{AB}[/math] as its hypotenuse.
c. Explain how you know that the triangle you formed contains a right angle. Use the button to check your answer.
d. Now rotate the triangle by clicking and dragging the point [math]B'[/math]. Rotate the triangle [math]90^\circ[/math] around the point [math]A(2,3)[/math]. Explain how you know you rotated the triangle [math]90^\circ[/math]. Check your answer with the new button if you are not sure.
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?