coordinate systems, question 1, grade 9

02/07/2016 Grade 9 892

1)

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

a) Plot the points: A(4,2), B(-2,2), and the line (d) : y = -x + 4

b) Calculate the coordinates of G, the midpoint of [OA].

c)

i) Determine the equation of the line (OA).

ii) let (D) be the perpendicular bisector of [OA], Verify that (D) : y = -2x + 5

d) Let M be the intersection point of (D) and (d),

  1. Justify why MO = MA.
  2. Show that the coordinates of M are (1,3).
  3. Prove that MOA is a right isosceles triangle.

e) Consider the line (L) : y = (m+3)x - 4, determine m in each of the following cases:

i) (L) passes thru (1,2).

ii) (L) is perpendicular to (d).