By Jacky Girardet
Booklet through Girardet, Jacky, Cridlig, Jean-Marie
Read Online or Download Panorama De LA Langue Francaise: Methode De Francais : Level 1 PDF
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Additional resources for Panorama De LA Langue Francaise: Methode De Francais : Level 1
Example text
Problem. Given two pOÎnts A and B in the plane, find the locus of points M whose distance from A Îs twice as great as from B. 'Notice that in the solution of this problem we have not resorled 10 a sketch. 27 Solution. Let us choose a system of coordinates on the plane such that the origin is located at the point A and the positive part of the x-axis lies along AB. We take the length of AB as the unit of length. Then the point A will have coordinates (0,0), and the point B will have the coordinates (1,0).
Compute the angles A, B, and C of the triangle ABC.
Let us take the point A as the origin and direct the x-axis from A to B. Then the point B will have the coordinates (c,O), where c is the length of the segment AB. Let the point C have the coordinates (q, hl, and let the center of the desired circJe have the coordinates (a, h). The radius of this circle we denote by R. We write down in coordinate language that the points A(O, 0), B(c,O), and C(q, h) lie on the desired circle: (c (q a)2 a2 + h2 R 2, a)2 + h2 R 2, + (II h)2 = R 2 • These conditÎons express the fact that the distance of each of the points A(O, 0), B(c, 0), and C(q, Il) from the center of the circle (a, h) is equal to the radius.