Problem 1. Consider the diagram below. Find an affine transformation T

Problem 1. (a) Consider the diagram below. Find an afne transformation T which maps the black triangle V onto the grey triangle W with vertex vi mapping to vertex w, for 1' = 0, 1, 2. (b) Now imagine that each point x in triangle V moves in a straight line at constant Speed [though the speed will be different for different points) so that it arrives at its image T[x) at time t = 1. Let TAX) be its position at time t [for 0 E t g 1). Find an expression for the transformation T}. In particular, this will allow you to see that it will be afne for all t. [c] Since the transformation T: is afne for all t, the image of the black triangle V at any time i will be a triangle though its shape will change with time. In fact there will be sorne moment at which it will in fact be a line segment, that is, the three points T,(vi) will be collinear. [Why is this?it is because the sequence V0,V1,V2 runs clockwise around the black triangle but Wu, W1,W2 runs counterclockwise around the grey triangle, so at some point the image of V; will have to cross the line containing the images of v0 and v1, and at that moment, the triangle will turn into a line segment] At what time it does this occur