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

$x,y=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}$

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

$\begin{gathered} x=\frac{x_2+x_1}{2} \\ 1=\frac{x_2+5}{2} \\ \text{cross multiply both sides} \\ 1\times2=x_2+5 \\ 2=x_2+5 \\ x_2=2-5 \\ x_2=-3 \end{gathered}$

now let's do the same for y

$\begin{gathered} y=\frac{y_2+y_1}{2} \\ -1=\frac{y_2+0}{2} \\ \text{cross multiply both sides} \\ 2\times-1=y_2+0_{} \\ -2=y_2 \\ y_2=-2 \end{gathered}$

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