7. Let (r1, Y1), (x2, Y2), (x3, Y3) be three points in R? that do not lie on a line. Let the curve T be the triangle with these three vertices, oriented by the given order of the vertices. You must leave r1, x2, X3, Y1, Y2; Y3 as variables; you do not get to choose specific numbers for them. Find the area bounded by the triangle T by computing the follow- ing line integral by parameterizing T and justify that this line integral computes the area. r dy. Simplify your answer until it is written as a single 3-by-3 determinant.

Question

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7. Let (r1, Y1), (x2, Y2), (x3, Y3) be three points in R? that do not lie on a
line. Let the curve T be the triangle with these three vertices, oriented
by the given order of the vertices. You must leave r1, x2, X3, Y1, Y2; Y3
as variables; you do not get to choose specific numbers for them.
Find the area bounded by the triangle T by computing the follow-
ing line integral by parameterizing T and justify that this line integral
computes the area.
r dy.
Simplify your answer until it is written as a single 3-by-3 determinant.
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Transcribed Image Text

7. Let (r1, Y1), (x2, Y2), (x3, Y3) be three points in R? that do not lie on a line. Let the curve T be the triangle with these three vertices, oriented by the given order of the vertices. You must leave r1, x2, X3, Y1, Y2; Y3 as variables; you do not get to choose specific numbers for them. Find the area bounded by the triangle T by computing the follow- ing line integral by parameterizing T and justify that this line integral computes the area. r dy. Simplify your answer until it is written as a single 3-by-3 determinant.