The coordinate system, question 1, Grade 10

01/03/2017 Grade 10 3,560

In a coordinate system  ,the following questions are independent:

  1. 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.
  2. Given : K(n2-1,3) , F(0,1) and G(4,5). For what values of n is K the midpoint of [FG]
  3. Does there exist a real number k s.t. the vector

    \overrightarrow u ({k^4} + 1,3)

    and the vector

    \overrightarrow v ( - 5,1)

    have the same direction?
  4. m is any real number s.t.

    \overrightarrow {AB}=(m-1)\overrightarrow  i+2\overrightarrow j

    and

    \overrightarrow{DC}=-\overrightarrow i+(m+2)\overrightarrow j

    . Determine m if ABCD is a trapezoid.
  5. 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.