Question

6) Endpoint: (5,0), midpoint: (1, -1)

Answer 1

hello

we're required to find the second end point from the given values

end point = (5, 0)

mid point = (1, -1)

to solve this problem, we'll need to use thw formula for mid-point

`x,y=(x_2+x_1)/(2),(y_2+y_1)/(2)`

now let's identify our variables

`\begin{gathered} x=1,y=-1, \\ x_1=5,y_1=0 \\ x_2=\text{ ?} \\ y_2=\text{ ?} \end{gathered}`

let's substitute in our values and solve respectively

`\begin{gathered} x=(x_2+x_1)/(2) \\ 1=(x_2+5)/(2) \\ \text{cross multiply both sides} \\ 1*2=x_2+5 \\ 2=x_2+5 \\ x_2=2-5 \\ x_2=-3 \end{gathered}`

now let's do the same for y

`\begin{gathered} y=(y_2+y_1)/(2) \\ -1=(y_2+0)/(2) \\ \text{cross multiply both sides} \\ 2*-1=y_2+0_{} \\ -2=y_2 \\ y_2=-2 \end{gathered}`

the values of the other end point are (-3, -2)