Question

Find the distance and the midpoint of (14,7) and (-12,-2)

Answer 1

distance = 27.51 (rounding to hundredth) OR 27.5 (rounding to tenth)

midpoint = (1, 2.5) (decimal form) OR (1, 5/2) (fraction form)

Explanation:

To find the distance, apply the distance formula. (refresh your page)

`d=√((x_2-x_1)^2+(y_2-y_1)^2)\\\text{Substitute the values.}\\d=√((-12-14)^2+(-2-7)^2)\\\text{Subtract inside the parenthesis.}\\d=√((-26)^2+(-9)^2)\\\text{Apply the powers.}\\d=√(676+81)\\\text{Add.}\\d=√(757)\\\text{Evaluate the square root.}\\d\approx27.51\text{ rounded to the nearest hundredth}\\d\approx27.5\text{ rounded to the nearest tenth}`

To find the midpoint, apply the midpoint formula.

`(x_m,y_m)=(x_1+x_2)/(2),(y_1+y_2)/(2)\\\text{Substitute the values.}\\(x_m,y_m)=(14+(-12))/(2),(7+(-2))/(2)\\\text{Add.}\\(x_m,y_m)=(2)/(2),(5)/(2)\\\text{Divide.}\\(x_m,y_m)=(1,2.5)`