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2 D 10670

1 3 4
Find the inverse of the affine transformation ¢ (X) = | ۱ X+ | |

State fundamental theorem of affine geometry.
Prove that an affine transformation maps straight lines to straight lines.

State Desargue’s theorem.
Find the equation of the line that passes through the point (1, 2, 3] and [2, - 1, 4].

Find the point of intersection of thelinesin RP? with equations x + 6y — 5z=0 and x -2y+z=0.
(8 x 3 = 24 marks)
Section B

Answer at least five questions.

Each question carries 5 marks.

All questions can be attended.
Overall Ceiling 25.

2 | 2
Let PQ be an arbitrary chord of the ellipse with equation > + a =1. Let M be the midpoint of
a

PQ. Prove that the following expression is independent of the choice of P and Q: Slope of
OM x Slope of PQ.

State and prove reflection properties of the ellipse.

Prove that the set of all affine transformations A(2) formsa group under the operation of composition

of functions.

Determine the image of the line y=2x under the affine transformation

०७) १0

Determine the affine transformation which maps the points (2,3), (1,6) and (3, — 1) to the points

(1,- 2), (2,1) and (- 3,5) respectively.

17003