Question

On the coordinate grid of a map. Jeff's house is located at (9,5). Hannah's house is at (-5,-5). Kenya's house is located at the midpoint between Jeff and Hannah's houses. What is the distance from Hannah's house to Kenya's house?

Answer 1

The midpoint formula is
`( x_(1) + x_(2) )/(2), ( y_(1)+ y_(2) )/(2)`
So just plug in the corresponding coordinates in the correct place to get the midpoint.
x_1=-5 ; x_2=9 ; y_1=-5 ; y_2=5
((-5 + 9)/2 , (-5 + 5)/2)
(4/2 , 0/2)
(2,0) is where Kenya's house is(which is the midpoint).

The distance formula is a bit more complicated than that. The distance formula is D=
`\sqrt{({y_(2)- y_(1) }^(2)) + ({ x_(2)- x_(1)}^(2) ) }`
In this case now, your looking for the distance from Hannah's house to Kenya's house.
D=
`\sqrt{(-5-2)^(2) + (-5-0)^(2) }`
=
`√(49+25)`
=
`√(74)` ≈8.6023