# The coordinate system, question 1, Grade 10

In a coordinate system ,the following questions are independent:

- Consider: M(x,y), A(2,-1), E(3,0) and I(0,1); Calculate x and y Knowing that I is the centroid of triangle MEA.
- Given : K(n
^{2}-1,3) , F(0,1) and G(4,5). For what values of n is K the midpoint of [FG] - Does there exist a real number k s.t. the vector
and the vector

have the same direction?

- m is any real number s.t.
and

. Determine m if ABCD is a trapezoid.

- Consider the points A(a,b), B(2,-1), and C(3,3). Determine a and b knowing that A is the point of intersection of (BC) and (D): y=2x.