coordinate systems ,question 2, grade 9

11/07/2016 Grade 9 4,091


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

  1. Plot A, B, and the line (d).
  2. Determine the coordinates of M, the midpoint of [AB].
  3. The line (d) cuts the (x'x) at E and the (y'y) at F. Verify that M, E, & F are collinear.
  4. Find the equation of the line (OB).
  5. Calculate the coordinates of I, the point of intersection of (d) and (OB).
  6. Verify that the equation of line (AB) is :  y=\frac{{-4}}{3}x+\frac{{10}}{3} .
  7. Deduce, graphically, the solution of the system
  8. \left\{ \begin{gathered}4x + 3y = 10 \hfill\\3x + y = 0 \hfill \\ \end{gathered} \right.

  9. Given (L) : y = (m-1)x + 3, find m so that (L) is perpendicular to (AB).