Question

Given direct line segment CD if point E divides CD three -fourths of the way form c to d find thw coordinates of a then plot e

Answer 1

E( -2, -1.5)

Step-by-step explanation:

First, we need to identify the coordinates of C and D, so the coordinates are:

C(1, 6)

D(-3, -4)

Now, if E divides CD three-fourths of the way from C to D, we can use the following equation to find the coordinates of E:

`\begin{gathered} E_x=x_1+(3)/(4)(x_2-x_1) \\ E_y=y_1+_{}(3)/(4)(y_2-y_1) \end{gathered}`

Where Ex is the coordinate of E in x, Ey is the coordinate of E in y, (x1, y1) are the coordinates of C, and (x2, y2) are the coordinates of D. So, replacing (x1, y1) by (1, 6) and (x2, y2) by (-3, -4), we get:

`\begin{gathered} E_x=1+(3)/(4)(-3-1)=1+(3)/(4)(-4)=1-3=-2 \\ E_y=6+(3)/(4)(-4-6)=6+(3)/(4)(-10)=-1.5 \end{gathered}`

So, the coordinates of point E is (-2, -1.5) and the graph is: