Question

Alyssa is playing a video game. Her character is on a quest to vanquish an evil sorcerer and his minions from the land. Her character is a wizard whose spells have a range of 6 meters.

The locations of objects in the game are stored by the computer program in terms of x and y
coordinates.
(5, 4) is the location of Alyssa's wizard.
(8, 7) is the location of Minion A
(2, -1) is the location of Minion B.
(9, 0) is the location of Minion C.

What Minions are in range of Alyssa’s wizard?

Answer 1

To determine which minions are in range of Alyssa's wizard, we need to calculate the distance between her wizard's location and the location of each minion using the distance formula: (final answer is at the bottom)

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the location of Alyssa's wizard, and (x2, y2) is the location of each minion.

For Minion A, d = sqrt((8-5)^2 + (7-4)^2) = sqrt(9+9) = sqrt(18) = 4.24 meters

For Minion B, d = sqrt((2-5)^2 + (-1-4)^2) = sqrt(9+25) = sqrt(34) = 5.83 meters

For Minion C, d = sqrt((9-5)^2 + (0-4)^2) = sqrt(16+16) = sqrt(32) = 5.66 meters

Since Alyssa's wizard's spells have a range of 6 meters, Minion A is in range, but Minion B and Minion C are not in range. Therefore, only Minion A is in range of Alyssa's wizard.