Question

Find the midpoint and the distance between these 2 points. (-4,8) and (6,-2)

Answer 1

Midpoint = (1,3)

Distance = 10√2

Explanation:

Midpoint

`Midpoint = \left((x_2+x_1)/(2),\:\:(y_2+y_1)/(2)\right)\\\\\left(x_1,\:y_1\right)=\left(-4,\:8\right),\:\left(x_2,\:y_2\right)=\left(6,\:-2\right)\\\\=\left((6-4)/(2),\:(-2+8)/(2)\right)\\\\=((2)/(2) , (6)/(2) )\\\\Simplify\\=\left(1,\:3\right)`

Distance

`Distance = √(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)\\\\(-4,8)=(x_1,y_1)\\(6,-2)=(x_2,y_2)\\\\d=√(\left(6-\left(-4\right)\right)^2+\left(-2-8\right)^2)\\\\d = √((6+4)^2+(-2-8)^2)\\ \\d = √((10)^2 +(-10)^2)\\ \\d = √(100+100) \\\\d = √(200)\\ \\d = 10√(2)`