Question

April is an avid chess player. She sets up a coordinate system on her chess board so she can record the position of the pieces during a game. In a recent game, April noted that her king was at (4,2) at the same time that her opponent's king was at (7,8). How far apart were the two kings? Round to the nearest tenth of a unit if necessary.

Answer 1

6.7

Explanation:

To solve this problem, we need to calculate the distance between two points in the XY coordinate plane.

The formula to calculate this distance is:

d = sqrt(dx^2 + dy^2)

where dx is the difference between the X coordinate of the points, dy is the difference between the Y coordinate of the points, and d is the distance.

(sqrt is the square root of what is in the parenthesis)

The first point (April's king) has X=4 and Y=2, the second point (the opponent's king) has X=7 and Y=8.

So, we have that dx = 4-7 = -3 and dy = 2-8 = -6

Now, we calculate the distance:

d = sqrt[ (-3)^2 + (-6)^2 ] = sqrt(9+36) = sqrt(45) = 6.7082 = 6.7