Question

model it
complete the problems about ordered pairs with negative coordinates.
3 the coordinate plane shows point a.
a. describe how to move along grid lines from the origin to point a
in two steps.
b. how can you use your answer to problem 3a to write the ordered
pair for point a? what is the ordered pair for point a?
c. plot and label point b(0, -3) in the coordinate plane. how do you know where
to plot point b?
4 a. what does the sign of the x-coordinate of a point tell you about the
location of the point in the coordinate plane?
b. what does the absolute value of the x-coordinate tell you?
5 reflect what does it mean when the x-coordinate of an ordered pair
is negative? what does it mean when the y-coordinate is negative?
discuss it
ask: what do all
points that are to the
right of the origin have
in common?
share: i can tell from
coordinates if a point
is above or below the
origin by...

Explanation:

Part 3a

Step1: Analyze the coordinate plane

Looking at the coordinate plane, point A is in the fourth quadrant. To move from the origin \((0,0)\) to point A, we first consider the x - direction (horizontal) and then the y - direction (vertical).

Step2: Determine the horizontal and vertical moves

From the origin, we move 2 units to the right along the x - axis (since the x - coordinate of point A is positive 2) and then 3 units down along the y - axis (since the y - coordinate of point A is negative 3). Or we could also move 3 units down first and then 2 units to the right.

Part 3b

Step1: Recall the definition of an ordered pair

An ordered pair \((x,y)\) is written as (horizontal move, vertical move) from the origin. The first number in the ordered pair is the x - coordinate (horizontal movement) and the second number is the y - coordinate (vertical movement).

Step2: Use the movement from 3a to find the ordered pair

From part 3a, if we moved 2 units right (positive x - direction) and 3 units down (negative y - direction), the x - coordinate \(x = 2\) and the y - coordinate \(y=- 3\). So the ordered pair for point A is \((2,-3)\).

Part 3c

Step1: Analyze the ordered pair \(B(0,-3)\)

For an ordered pair \((x,y)\), the x - coordinate tells us the horizontal position and the y - coordinate tells us the vertical position. When \(x = 0\), the point lies on the y - axis.

Step2: Determine the position of point B

Since \(x = 0\), we start at the origin and move 0 units horizontally (stay on the y - axis). Then, since \(y=-3\), we move 3 units down along the y - axis. So point B is on the y - axis, 3 units below the origin.

Part 4a

Answer:

s:
3a. Move 2 units right and then 3 units down (or 3 units down and then 2 units right) from the origin.
3b. The ordered pair is \(\boldsymbol{(2,-3)}\) (using the movement to get \(x\) (horizontal) and \(y\) (vertical) coordinates).
3c. Point \(B(0,-3)\) is on the y - axis, 3 units below the origin (since \(x = 0\) (on y - axis) and \(y=-3\) (3 units down)).
4a. If the x - coordinate is positive, the point is to the right of the y - axis; if negative, to the left; if 0, on the y - axis.
4b. The absolute value of the x - coordinate tells the distance of the point from the y - axis.

1. A negative x - coordinate means the point is left of the y - axis; a negative y - coordinate means the point is below the x - axis.