Question

Find the coordinates of the missing endpoint if E is the midpoint of DF F(5,8), E(4,3) D=

Answer 1

The coordinates of D is;

`(3,-2)`

Step-by-step explanation:

The question can be illustrated diagramatically as;

The drawing is not to scale. it is just a way of explainuing the scenario.

To find the coordinates of the end point D(x,y).

Let us apply the mid point formula;

`\begin{gathered} \bar{x}=(x_1+x_2)/(2) \\ x_1=\bar{2x}-x_2 \end{gathered}`

The same applys to y coordinates.

Given;

`\begin{gathered} E(4,3)=(\bar{x},\bar{y}) \\ F(5,8)=(x_2,y_2) \\ D=(x_1,y_1) \end{gathered}`

Substituting we have;

`\begin{gathered} x_1=\bar{2x}-x_2 \\ x_1=2(4)-5_{} \\ x_1=8-5 \\ x_1=3 \end{gathered}`

Also,

`\begin{gathered} y_1=\bar{2y}-y_2 \\ y_1=2(3)-8 \\ y_1=6-8 \\ y_1=-2 \end{gathered}`

Therefore, the coordinates of D is;

`(3,-2)`