1. Let F(x, y) = (3x – 2, 3y – 10). Draw a triangle ABC on graph paper and then draw the image of the triangle A'B'C' under F. Draw the lines (not segments) AA', BB', CC'. Are they concurrent. Where do they intersect? Is F a dilation?
2. Investigate F algebraically. Find the fixed point of F by solving (u, v) = F(u, v). Use the fixed point to regroup the formula for F so that it is clearly a dilation.

On graph paper, draw a line through (0,0) with nonzero slope. Pick two points on the line and draw the feet of the perpendiculars to the x-axis and y-axis. Show how the proportional relations in the figure lead to the equation of the line in terms of x and y.

In each case, draw the figures and find the centers of any dilations that take one of the two figures to the other.

1. Two parallel segments of different length.
2. Two circles of different size.
3. A triangle ABC with midpoint triangle A'B'C.
4. The same triangle ABC and triangle AC'B'.
5. A parallelogram and itself.