Day 2- Real World- Midpoint While planning the layout of her yard, Laura created a grid

system representing her backyard. On the grid, Laura placed

the center of a herb garden at the coordinates (3.14) and wants

to place a bird bath at the point (7,29). If Laura wants to

position the center of a flower garden so that the bird bath is

halfway between the herb and flower gardens, at what

coordinates should the center of the flower garden be placed?

(11, 150

O (11,44)

O (4,44)

O (4,15)

Help

Point of the flower garden  R ( 11, 44 )

Step-by-step explanation:

Let´s call   P (  3, 14 ) The center of the herb garden, and Q ( 7 , 29 ) the birdbath point

Differences in coordinates of these two points are:

x axis        7 - 3   = 4

y axis     29 - 14  = 15

Then the point Q ( x , y ) will be at:  Q ( 11, 44)

x axis    x = 11 because    7 + 4 = 11 means that the coordinate 7 is just halfway way between coordinates (x)  3 and 11  ( 4 above 3, and 4 below 11)

Reasoning the same way we conclude y = 44 in this case 29 is just halfway between coordinates  (y) 14 and 44 ( 15 above 14 and 15 below 44)

We can probe getting distance d₁  between P and Q  and d₂ distance between Q and R as:

d₁ = √ (7-3)² + ( 29-14)²

d₁ = √ 16 + 225

d₂ = √ (11 - 7)² +  ( 44 - 29)²

d₂ = √ 16 + 225

55 degrees because 55+55=110 degrees