Answer
The coordinates of the meeting point of Kim and Danielle is (8, 2.5).
On the map, this coordinate corresponds to inside the Jewel accessories' store. So, this is where their meeting point is going to be.
Step-by-step explanation
We are told that Kim is meeting Danielle at the mall.
Kim starts at the southern entrance to the mall which is at coordinate (16, 0)
And Danielle starts at the Western entrance to the mall at coordinates (0, 5)
We are now told to calculate the coordinates of where they will meet up if they are to meet at the midpoint of their respective starting positions, assuming that they can walk through walls and all.
Mathematically, if a point P(x, y) divides the coordinates (x₁, y₁) and (x₂, y₂) internally in the ratio m:n then point P(x, y) is given as
x = [(mx₂ + nx₁)/(m + n)]
y = [(my₂ + ny₁)/(m + n)]
For this question,
(x₁, y₁) and (x₂, y₂) is (16, 0) and (0, 5) respectively
And m:n is 1:1, since the meeting point for these two friends is the midpoint of the starting points which means that that meeting point divides the distance between them equally in the ratio 1:1
x₂ = 0
x₁ = 16
y₂ = 5
y₁ = 0
m = 1
n = 1
We can now calculate the coordinates of this midpoint, starting with the x-coordinate
x = [(mx₂ + nx₁)/(m + n)]
x = [(1×0 + 1×16)/(1 + 1)]
x = (0 + 16)/2
x = (16/2) = 8
Then, we can calculate the y-coordinate
y = [(my₂ + ny₁)/(m + n)]
y = [(1×5 + 1×0)/(1 + 1)]
y = (5 + 0)/2
y = (5/2) = 2.5
The coordinates of the meeting point of Kim and Danielle is (8, 2.5).
On the map, this coordinate corresponds to inside the Jewel accessories' store. So, this is where their meeting point is going to be.
Hope this Helps!!!