On a coordinate grid map jaff's house is located at (9,5.). Hannah's house is at (-5,-5). Kenya's house is at the midpoint between Jeff and Hannah's. what's the distance.
well, it's half the distance from (9,5) to (-5,5)
Note that both points are on the line y=5, so the distance is just 14.
To find the distance between Kenya's house and the other two houses, we first need to determine the coordinates of Kenya's house. Since Kenya's house is at the midpoint between Jeff and Hannah's houses, we can find it by taking the average of their x-coordinates and the average of their y-coordinates.
The x-coordinate of Kenya's house (Kx) can be found by taking the average of Jeff's x-coordinate (Jx) and Hannah's x-coordinate (Hx), so:
Kx = (Jx + Hx) / 2
= (9 + (-5)) / 2
= 4 / 2
= 2
The y-coordinate of Kenya's house (Ky) can be found similarly by taking the average of Jeff's y-coordinate (Jy) and Hannah's y-coordinate (Hy), so:
Ky = (Jy + Hy) / 2
= (5 + (-5)) / 2
= 0 / 2
= 0
Therefore, the coordinates of Kenya's house are (2, 0).
Now that we have the coordinates of Kenya's house, we can find the distance between Kenya's house and the other two houses using the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances:
Distance between Jeff's house and Kenya's house:
√((Kx - Jx)^2 + (Ky - Jy)^2)
= √((2 - 9)^2 + (0 - 5)^2)
= √((-7)^2 + (-5)^2)
= √(49 + 25)
= √74
≈ 8.60 units
Distance between Hannah's house and Kenya's house:
√((Kx - Hx)^2 + (Ky - Hy)^2)
= √((2 - (-5))^2 + (0 - (-5))^2)
= √((2 + 5)^2 + (0 + 5)^2)
= √((7)^2 + (5)^2)
= √(49 + 25)
= √74
≈ 8.60 units
Therefore, the distance between Kenya's house and the other two houses is approximately 8.60 units.