coordinates

Given the points C(-1,-5) and D(-7,11), find the coordinates of point E on CD such that the ratio of CE to ED is 5:3

Hello Guest!

\(y_E=y_C+\frac{3}{5}(y_D-y_C)\\ y_E=-5+ \frac{3}{5}(11-(-5))=\color{blue}4.6\)

\(x_E=x_C-\frac{3}{5}(x_C-x_D)\\ x_E=-1-\frac{3}{5}(-1-(-7))=\color{blue}-4.6\)

The coordinates of point E are E (-4.6,4.6)

  !

x    from -1 to -7 is  distance of -6       5 / (5+3)  = 5/8 ths  of this is added to -1 to get   x = -4 6/8 = -4.75

y    from -5 to 11 is  distance of 16      5/8 of this is added to -5 to get    y = 5                               

                      (  -4.75,5 )