= I. Let P (-2.3). Q = (3.13), R=P+Q. v=Q-P and P+[e]. Moreover, let X=(1, 2)...

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= I. Let P (-2.3). Q = (3.13), R=P+Q. v=Q-P and P+[e]. Moreover, let X=(1, 2) be any point of E. 1. Find (P.Q). 2. Find v. 3. Write the equation of the line in the form ar+by+c=0. 4. Find A and a unit vector a st. the line 4+ [a] is perpendicular to (and passes through R. 5. Find B (distinct from R) and a unit vector 3 s.t. the line B+[8] is parallel to and passes through R. 6. What is (X)? 7. If ml and Pm, what is (X)? What is 2(X)? 8. If G is the glide reflection 7/2, what is G(X)? passing through R. Find d(l,n). 9. Let n be the line parallel to 10. Let n be as in Q9. What is 2 (X)? What is (X)? II. Let X = [4] Find the image of X under the following isometries. 1. Q, where is the line with equation 1-2y-6=0 2. Te, where Tr - (2) - B)] 3. G. the glide reflection defined by in (1) and 7, where w= (4.2) 4. R, the (counterclockwise) rotation about the origin at an angle /3 = I. Let P (-2.3). Q = (3.13), R=P+Q. v=Q-P and P+[e]. Moreover, let X=(1, 2) be any point of E. 1. Find (P.Q). 2. Find v. 3. Write the equation of the line in the form ar+by+c=0. 4. Find A and a unit vector a st. the line 4+ [a] is perpendicular to (and passes through R. 5. Find B (distinct from R) and a unit vector 3 s.t. the line B+[8] is parallel to and passes through R. 6. What is (X)? 7. If ml and Pm, what is (X)? What is 2(X)? 8. If G is the glide reflection 7/2, what is G(X)? passing through R. Find d(l,n). 9. Let n be the line parallel to 10. Let n be as in Q9. What is 2 (X)? What is (X)? II. Let X = [4] Find the image of X under the following isometries. 1. Q, where is the line with equation 1-2y-6=0 2. Te, where Tr - (2) - B)] 3. G. the glide reflection defined by in (1) and 7, where w= (4.2) 4. R, the (counterclockwise) rotation about the origin at an angle /3