contestada

2)
8
7
A town has four coffee shops, A, B, C and D. An
entrepreneur wishes to open a new shop in the town but
would like it to be as far as possible from all the other
four coffee shops.
The Voronoi diagram of the coffee shops is shown to the right
6
D
5
4.
P
a) What are the coordinates of coffee shop C?
3
B
2
1
b) What is the equation of line QP?
0
1
2
3
4
6
9 10
c) What is the equation of the perpendicular bisector of CD?
d) What are the coordinates of point P?

Respuesta :

MrRoyal

The graph is an illustration of several linear functions.

What are linear functions?

These are functions that have a constant rate or slope

(a) The coordinates of coffee shop C

Coffee shop C is located at (8,2)

Hence, the coordinates of coffee shop C is (8,2)

(b) The equation of line QP

Line QP passes through points (5,3.5) and (4.5,4.5)

Start by calculating the slope of the line

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{4.5 - 3.5}{4.5 - 5}[/tex]

[tex]m = -2[/tex]

So, the equation of the line is:

[tex]y = m(x -x_1) + y_1[/tex]

This gives

[tex]y = -2(x -5) + 3.5[/tex]

[tex]y = -2x +10 + 3.5[/tex]

[tex]y = -2x +13.5[/tex]

Hence, the equation of line QP C is [tex]y = -2x +13.5[/tex]

(c) The equation of the perpendicular bisector of CD

The perpendicular bisector of CD is a horizontal line that passes through y = 3.5

Hence, the equation of the perpendicular bisector of CD is y = 3.5

(d) The coordinates of coffee point P

Point P is located at (5,3.5)

Hence, the coordinates of point P is (5,3.5)

Read more about linear graphs at:

https://brainly.com/question/14323743

Ver imagen MrRoyal

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