Answer:
distance = 27.51 (rounding to hundredth) OR 27.5 (rounding to tenth)
midpoint = (1, 2.5) (decimal form) OR (1, 5/2) (fraction form)
Step-by-step explanation:
To find the distance, apply the distance formula. (refresh your page)
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\text{Substitute the values.}\\d=\sqrt{(-12-14)^2+(-2-7)^2}\\\text{Subtract inside the parenthesis.}\\d=\sqrt{(-26)^2+(-9)^2}\\\text{Apply the powers.}\\d=\sqrt{676+81}\\\text{Add.}\\d=\sqrt{757}\\\text{Evaluate the square root.}\\d\approx27.51\text{ rounded to the nearest hundredth}\\d\approx27.5\text{ rounded to the nearest tenth}[/tex]
To find the midpoint, apply the midpoint formula.
[tex](x_m,y_m)=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\\\text{Substitute the values.}\\(x_m,y_m)=\frac{14+(-12)}{2},\frac{7+(-2)}{2}\\\text{Add.}\\(x_m,y_m)=\frac{2}{2},\frac{5}{2}\\\text{Divide.}\\(x_m,y_m)=(1,2.5)[/tex]
