Question

5. MAPPING Ben and Kate are making a

map of their neighborhood on a piece of
graph paper. They decide to make one
unit on the graph paper correspond to
100 yards. First, they put their homes
on the map as shown below.

a. How many yards apart are Kate's and Ben's homes?

b. Their friend Jason lives exactly halfway between Ben and Kate. Mark the location of Jason's home on the
map. if my answers are wrong, correct me. i just used a pdf and idk if they’re right. ty ❤️

Answer 1

a. 1,000 yards

b. (2, -1)

Explanation:

Coordinates of Ben's House = (6, 2)

Coordinates of Kate's House = (-2, -4)

a. Number of yards between Kate and Ben's House using instance formula,
`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`.

`d = √((6 -(-2))^2 + (2 -(-4))^2)`

`d = √((8)^2 + (6)^2)`

`d = √(64 + 36)`

`d = √(100)`

`d = 10 units`

1 unit = 100 yards

Therefore, 10 units = 1,000 yards.

Kate and Ben's House are 1,000 yards apart.

b. Since Jason's home is halfway between Ben and Kate's House, therefore, Jason's location is the midpoint between Ben and Kate's House. Use the midpoint formula to calculate the coordinates of Jason's location on the map, using (6, 2) and (-2, -4).

`M((x_1 + x_2)/(2), (y_1 + y_2)/(2))`

Plug in the values

`M((6 +(-2))/(2), (2 +(-4))/(2))`

`M((4)/(2), (-2)/(2))`

`M(2, -1)`