Question

The Voronoi diagram below shows the locations of the four post offices P_{1} , P_{2} P_{3} , and P_{4}in a city.y(km)8P_{3}P2r (km)6P_{1}PKatie's apartment lies inside the shaded circle shown on the diagram.(a) Write down the post office nearest to Katie's apartment.P is located at coordinates (3-6), and the edge between P and P_{i} has the equation y = - 5/3 * x = 16/3(b) Determine the location of PPa is located at coordinates (1.7).3(c) Find the gradient. A. of the edge between P, and P.

Answer 1

Given -

Voronoi diagram:

To Find -

(a) Write down the post office nearest to Katie's apartment.

(b) Determine the location of P4

(c) Find the gradient k. of the edge between P3 and P4

Step-by-Step Explanation -

(a)

We can see from the voronoi diagram that the center of the x-axis where the circle covers is where Katie's apartment is located.

It is located near P4.

So,

P4 is nearest to Katie's apartment.

(b)

The location of P4:

(2, -3)

(c)

`k\text{ = }\frac{Y_2\text{ - Y}_1}{X_2\text{ - X}_1}\text{ = }(7)/(50)`

Final Answer -

(a) The post office nearest to Katie's apartment = P4

(b) The location of P4 = (2, -3)

(c) The gradient k of the edge between P3 and P4 = 7/50