Question

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

Answer 1

Point of the flower garden R ( 11, 44 )

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