# Coordinate systems, grade 9, question6

In an orthonormal system of axes (x’x) and (y’y):

- Plot :A(1,3), B(-4,0), and C(5,0) and draw : (d):y=3x.
- Verify that A belongs to (d).
- Find the equation of a st.line (L) parallel to (d) and cutting (x’x) at a point M of abscissa 3
- (d) intersects (AC) in N, Calculate AO then MN.
- H is the orthogonal projection of A on (x’x). Find the center and the radius of the circle circumscribed about triangle AHB.
- Consider I(n
^{2}-1, 1.5), find the values of n if I is the midpoint of [AC]. - Given L(2m-1,m); determine m if A,O,L are collinear.