Question

5. MAPPING Ben and Kate are making a

Answer 1

Answer:

a. 1,000 yards

b. (2, -1)

Step-by-step 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, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

$d = \sqrt{(6 -(-2))^2 + (2 -(-4))^2}$

$d = \sqrt{(8)^2 + (6)^2}$

$d = \sqrt{64 + 36}$

$d = \sqrt{100}$

$d = 10 units$

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).

$M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

Plug in the values

$M(\frac{6 +(-2)}{2}, \frac{2 +(-4)}{2})$

$M(\frac{4}{2}, \frac{-2}{2})$

$M(2, -1)$