Answer:
The mid point of ST is (1,5) and ST = 10 units
Step-by-step explanation:
It is given that,
S(-3,2) and T(5,8). We need to find the coordinates of the midpoint of ST and also ST.
Let (x,y) be the mid point of ST. Using mid-point formula we get :
[tex](x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
We have, x₁ = -3, x₂ = 5, y₁ = 2 and y₂ = 8
So,
[tex](x,y)=(\dfrac{-3+5}{2},\dfrac{2+8}{2})\\\\(x,y)=(1,5)[/tex]
(1,5) is the midpoint of ST.
Using distance formula to find ST as follows :
[tex]ST=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\ST=\sqrt{(5-(-3))^2+(8-2)^2} \\\\ST=10\ \text{units}[/tex]
Hence, the mid point of ST is (1,5) and ST = 10 units.
