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Town L lies to the west of Town M. Town D lies to the northeast of Town L. Town A lies to the west of Town D. Town R lies to the east of Town D. What is the position of Town R with respect to Town L?
Northwest
Northeast
Southwest
Southeast
Northeast
Place L at the origin (0,0) and use Cartesian coordinates to track positions: M is at (+x, 0), D is at (+x, +y) relative to L, and R is east of D, ensuring R is northeast of L.
Place L at the origin (0,0) and use Cartesian coordinates to track positions: M is at (+x, 0), D is at (+x, +y) relative to L, and R is east of D, ensuring R is northeast of L.
Establish Reference Points
Let Town L be at (0, 0). Since Town M is to the west of M, L is at (xLтАЛ, y) and M is at (xMтАЛ, y) where xLтАЛ < xMтАЛ. Simplified: L=(0,0), M=(1,0).
Plot Town D and A
Town D is northeast of L. This means D is at a coordinate (xDтАЛ, yDтАЛ) where xDтАЛ > 0 and yDтАЛ > 0. Town A is west of D, so A is at (xAтАЛ, yDтАЛ) where xAтАЛ < xDтАЛ.
Determine Position of R
Town R lies to the east of Town D. Since D is already northeast of L (positive x and positive y relative to L), moving further east (increasing x) keeps R in the northeast quadrant relative to L.
A: Northwest is incorrect as R has a positive X-offset from D which is already at a positive X-offset from L. C: Southwest is incorrect because both D and R maintain positive Y-offsets. D: Southeast is incorrect because R's Y-coordinate is derived from D, which is northeast of L.
B is correct because Town D is already in the Northeast quadrant relative to L, and since R is to the East of D, it maintains its position in the Northeast quadrant relative to L.
When solving direction problems, always fix your starting point as (0,0) on a Cartesian plane to visualize the movement precisely without getting confused by verbal descriptions.
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