Question

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.

Explanation:

Part (a)

Step1: Analyze x - coordinate

The x - coordinate of the point \((- 3,1)\) is \(-3\). In a coordinate plane, negative x - values mean moving to the left (west) from the origin. So, for the x - component, we move 3 units left.

Step2: Analyze y - coordinate

The y - coordinate of the point \((-3,1)\) is \(1\). Positive y - values mean moving up (north) from the origin. So, for the y - component, we move 1 unit up.

Step1: Determine the x - coordinate

Moving west (left) on the x - axis corresponds to negative x - values. If we move 2 units west from the origin (Spyglass Rock is at the origin \((0,0)\)), the x - coordinate is \(- 2\).

Step2: Determine the y - coordinate

Moving south on the y - axis corresponds to negative y - values. If we move 4 units south from the origin, the y - coordinate is \(-4\).

Step3: Plot the point

The coordinates of the black pearl are \((-2,-4)\). To plot this point, start at the origin, move 2 units to the left (west) along the x - axis and then 4 units down (south) along the y - axis.

Answer:

For part (a), the first blank is "left" and the second blank is "up".

Part (b)