MATH235 Lecture Notes - Lecture 27: Asymptote

4. Let A = (1,2), let B = (3,1). Parametrize the line segment from A to B Example. A parametrization of the line segment from A to B can be obtained by letting ã and b be the position vectors for the points A and B and using the formula γ(t) = a + t(b-d), t e lo, 1] Note that γ(0) = a (= A) and γ(1) = b (= B) and if t is between 0 and 1, then γ(t) is a point on the line through A, B and lies between these two points. For example, if A = (2,5) and B (13), then = (2,5) + t(-1,-2) =(2-t,5-2). Exercise: Evaluate γ(t) for t each of 0, 1/41/23/21 and plot the resulting points. 5. Let T be triangle with vertices A = (1,0), B = (3,0), C= (3,2). Let F(x, y) = P(x,y)T + Q(x, y) with P(z, y)-12 , Q(z, y) = x-y. Evaluate dA directly (without using Green's Theorem)