Given the line segment CD, point E divides CD three-fourths of the way from C to D
If you graph segment CD and divide it in four, count starting from C three cuarters and you'll get the location of point E
To calculate the coordinates of E, first you have to determine the distance between points C and D.
C (1,6) D (-3, -4)
Distance over the x-axis:
[tex]x_C-x_D=1-(-3)=4[/tex]
Multiply it by 3/4
[tex]4\cdot\frac{3}{4}=3[/tex]
The x-coordinate of Point E
Subtract the calculated distance to the x-coordinate of point C
[tex]\begin{gathered} x_{E=}x_C-3=1-3 \\ x_E=3-2 \end{gathered}[/tex]
Distance over the y-axis:
[tex]y_C-y_D=6-(-4)=10[/tex]
Multiply it by 3/4 to determine the distance of E over the y-axis
[tex]10\cdot\frac{3}{4}=\frac{15}{2}[/tex]
Subtract it to the y-coordinate of C to determine the coordinate of E
[tex]\begin{gathered} y_E=y_C-\frac{15}{2}=6-\frac{15}{2} \\ y_E=-\frac{3}{2} \end{gathered}[/tex]
Point E is in coordinates (-2,-3/2)
