Question

explore the four-quadrant coordinate plane
understand: what do negative coordinates in an ordered pair mean?
model it
complete the problems about the coordinate plane.
1 a treasure map is drawn in the coordinate plane with spyglass rock at the origin. the x - axis points east and the y - axis points north.
a. the map states that a diamond is located at (1, 3). plot a point to show the location of the diamond. label the point with its coordinates.
b. the map says a diamond can be found 4 units east and 2 units north of spyglass rock. plot a point to show the location of the diamond and label the point with its coordinates.
2 to show locations west and south of spyglass rock, the axes in the coordinate plane can be extended to show negative numbers. the axes intersect at the origin and divide the coordinate plane into four regions, or quadrants.
a. to plot the point for a ruby at (-3, 1), move 3 units _______ and 1 unit _______ from the origin.
b. the map says a black pearl can be found 2 units west and 4 units south of spyglass rock. plot a point to show the location of the black pearl and label the point with its coordinates.
discuss it
ask: why does it make sense that the x - coordinate of a point to the left of the origin is negative?
share: i think that a negative y - coordinate means that...

Explanation:

Step1: Analyze the coordinate system

The x - axis points east (positive x - direction) and west (negative x - direction), and the y - axis points north (positive y - direction) and south (negative y - direction). The origin is Spyglass Rock.
For the point \((- 3,1)\), the x - coordinate is \(-3\) and the y - coordinate is \(1\).

Step2: Determine the direction of movement for x - coordinate

Since the x - coordinate is \(-3\) and the positive x - direction is east, a negative x - coordinate means we move in the opposite direction of east, which is west. So we move 3 units west for the x - component.

Step3: Determine the direction of movement for y - coordinate

The y - coordinate is \(1\), and the positive y - direction is north. So we move 1 unit north for the y - component.

Answer:

west; north