Exercise 7
In an orthonormal system of axes (x'Ox, y'Oy), consider the points A (2 ; 0), B (0 ; 4) and E (- 4 ; 0).
Let (d) be the line with equation y=-2x+4.
1) Plot the points A, B and E.
2) Verify that A and B are two points on (d), then draw (d).
3) Let (d') be the line passing through E and perpendicular to (d).
Verify that y=-x+2 is the equation of (d').
2
4) The line (d') intersects (y'Oy) at H (0; 2) and intersects (d) at F.
a. Verify that the coordinates of F are
b. Show that H is the orthocenter of triangle EAB.
c. Prove that (AH) is perpendicular to (EB).