4 the coordinate plane shows point j
a. describe how to move from the origin to point j.
b. how can you use your answer to problem 4a to write the ordered pair for point j? what is the ordered pair for point j?
c. plot and label point k(-4, -5) in the coordinate plane. how do you know where to plot point k?
5 a. what does the sign of the y-coordinate of a point tell you about the location of the point in the coordinate plane?
b. what does the absolute value of the y-coordinate tell you?

Question

Accepted Answer

### Part 4a
# Explanation:
## Step1: Analyze the x - movement
The origin is $(0,0)$. Looking at the coordinate plane, point $J$ is on the x - axis. To move from the origin to point $J$, we move along the x - axis. Since it is to the left of the origin (negative x - direction), we move 3 units to the left (or 3 units in the negative x - direction). And since it is on the x - axis, the y - movement is 0 (we don't move up or down).
## Step2: Describe the movement
So, to move from the origin to point $J$, we move 3 units to the left (in the negative x - direction) and 0 units up or down (along the y - axis).
# Answer: Move 3 units to the left (and 0 units up/down) from the origin.

### Part 4b
# Explanation:
## Step1: Recall ordered pair definition
An ordered pair $(x,y)$ is written as (x - coordinate, y - coordinate), where the x - coordinate is the horizontal movement from the origin and the y - coordinate is the vertical movement from the origin.
## Step2: Determine coordinates from movement
From part 4a, the horizontal (x) movement is - 3 (since we moved 3 units left, which is negative in the x - axis) and the vertical (y) movement is 0 (since we didn't move up or down). So the ordered pair is $(-3,0)$.
# Answer: The x - coordinate is the horizontal movement, y - coordinate is vertical movement. Ordered pair: $(-3,0)$

### Part 4c
# Explanation:
## Step1: Analyze the ordered pair $(-4,-5)$
An ordered pair $(x,y)$ means we move $x$ units horizontally and $y$ units vertically from the origin. For $x=-4$, we move 4 units to the left (negative x - direction) from the origin. For $y = - 5$, we move 5 units down (negative y - direction) from the origin.
## Step2: Plot the point
First, start at the origin $(0,0)$. Move 4 units to the left along the x - axis (to $x=-4$). Then, from that position, move 5 units down along the y - axis. That is where point $K(-4,-5)$ should be plotted. We know this because the x - coordinate tells the horizontal position (left/right) and the y - coordinate tells the vertical position (up/down) relative to the origin.
# Answer: Move 4 left, 5 down from origin. Plot at intersection of $x = - 4$ (left 4) and $y=-5$ (down 5).

### Part 5a
# Explanation:
## Step1: Recall coordinate plane quadrants
In the coordinate plane, the y - axis divides the plane into upper (positive y) and lower (negative y) regions. If the y - coordinate is positive, the point is above the x - axis (in the upper half - plane, which includes Quadrants I and II). If the y - coordinate is negative, the point is below the x - axis (in the lower half - plane, which includes Quadrants III and IV). If the y - coordinate is 0, the point is on the x - axis.
# Answer: A positive y - coordinate means the point is above the x - axis; negative means below; 0 means on the x - axis.

### Part 5b
# Explanation:
## Step1: Recall absolute value definition
The absolute value of a number $|a|$ is the distance of the number from 0 on the number line. For the y - coordinate, $|y|$ is the distance of the point from the x - axis (since the y - coordinate measures vertical distance from the x - axis).
# Answer: The absolute value of the y - coordinate tells the distance of the point from the x - axis.

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QUESTION IMAGE

Question

Explanation:

Part 4a

Step1: Analyze the x - movement

Step2: Describe the movement

Step1: Recall ordered pair definition

Step2: Determine coordinates from movement

Step1: Analyze the ordered pair \((-4,-5)\)

Step2: Plot the point

Answer:

Part 4b