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 Hanna…

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asked Feb 5, 2021 132k views

2 Answers

Moudy · Answer 1 · 2021-02-09T15:53:12+0000

The distance from Hannah's house to Kenya's house is 8.6 units.

Explanation:

It is given that,

Kenya's house is located at the midpoint between Jeff and Hannah's houses.

Kenya's house = Midpoint of (9,5) and (-5,-5)

The formula to find the midpoint is that :

Midpoint =
((x1+x2) /2 , (y1+y2)/2)

Here, (x1,y1) = (9,5) and (x2,y2) = (-5,-5)

Midpoint =
((9-5)/2, (5-5/2))

⇒
(4/2 , 0/2)

⇒
(2,0)

Therefore, the Kenya's house is located at (2,0).

To find the distance from Hannah's house to Kenya's house :

The distance between Hannah's house located at (-5, -5) and Kenya's house located at (2,0) must be found using the distance formula.

The distance formula is given by :

Distance =
$\sqrt{(x2-x1)^(2) + (y2-y1)^(2) }$

Here, (x1,y1) = (-5,-5) and (x2,y2) = (2,0).

Distance =
$\sqrt{(2+5)^(2)+(0+5)^(2) }$

⇒
$\sqrt{7^(2) + 5^(2) }$

⇒
√(49+25)

⇒
√(74)

⇒ 8.6 units.

Therefore, the distance from Hannah's house to Kenya's house is 8.6 units.