# coordinate systems ,question 2, grade 9

2)

In an orthonormal system of axes (x'x) and (y'y) of center O, given the points A(4,-2); B(-2,6) and the line (d):y=4x-2

- Plot A, B, and the line (d).
- Determine the coordinates of M, the midpoint of [AB].
- The line (d) cuts the (x'x) at E and the (y'y) at F. Verify that M, E, & F are collinear.
- Find the equation of the line (OB).
- Calculate the coordinates of I, the point of intersection of (d) and (OB).
- Verify that the equation of line (AB) is : .
- Deduce,
**graphically**, the solution of the system - Given (L) : y = (m-1)x + 3, find m so that (L) is perpendicular to (AB).