It is expected that students will:

• solve problems involving distances between points and lines

The lines are parellel. Determine the vertical distance between the two lines, the horizontal disstance between the two lines and the shortest distance between the two lines.

• verify and prove assertions in plane geometry, using coordiante geometry

Given A = (-1, 3), B = (0, 5) and C = (-2, 6):
a) Verify that ABC is a right-angled triangle.
b) Is ABC isosceles? Justify your assertion.
c) If M is the midpoint of AB and N is the midpoint of AC, prove that MN is parallel to BC.
D) Find a point D so that ABCD is a parallelogram. Prove that ABCD is not a rectangle.

*Use coordinate geometry to prove that:
a) the diagonals of an parallelogram bisect one another in their midpoints
b) if ABC is an triangle, with M as the midpoint of AB and N as the midpoint of AC, then MN is parallel to BC and is half its length

Use coordinate geometry to divide the line segment with end points A(4, 7) and B(-3, 8) into five congruent parts.