Question: Let R2 be a line, and p a point. A perspective map takes a point x R2 to the point q that is the intersection

Let „“ Š‚ R2 be a line, and p ˆ‰ „“ a point. A perspective map takes a point x ˆˆ R2 to the point q ˆˆ „“ that is the intersection of „“ with the line going through p and x. If the line is parallel to „“ then the map is not defined. Find the formula for the perspective map when
(a) „“ is the x axis and p = (0, 1)T,
(b) „“ is the line y = x and p = (1, 0)T.
Is either map affine? An isometry?

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