Question

2-40 one of the topics you will review in this course is reading graphs. look at the graph at the right. this graph shows positive and negative values on both axes. it divides the flat surface into four parts, or quadrants, and therefore is called a four - quadrant graph.
a) the coordinates (the x - and y - values) for point a are (-3, 5). explain how these numbers tell you the position of point a using the graph.
b) name the coordinates (x, y) for points b and c.
c) if samantha moved point a 9 units down and 6 units to the right, at what point would she end up?

Explanation:

Step1: Understand coordinate - axis meaning

In a two - dimensional coordinate system, the x - value represents the horizontal position and the y - value represents the vertical position. For point A with coordinates (-3, 5), the x - value of - 3 means it is 3 units to the left of the origin (since negative x - values are to the left of the y - axis), and the y - value of 5 means it is 5 units above the origin (since positive y - values are above the x - axis).

Step2: Determine coordinates of B

Looking at the position of point B, it is 3 units to the left of the origin (x=-3) and 5 units below the origin (y = - 5). So the coordinates of B are (-3,-5).

Step3: Determine coordinates of C

Point C is 5 units to the right of the origin (x = 5) and 2 units below the origin (y=-2). So the coordinates of C are (5,-2).

Step4: Calculate new position of A

If point A(-3, 5) is moved 9 units down, the new y - value is \(y=5 - 9=-4\). If it is moved 6 units to the right, the new x - value is \(x=-3 + 6 = 3\). So the new point is (3,-4).

Answer:

a) The x - value of - 3 means point A is 3 units to the left of the origin and the y - value of 5 means it is 5 units above the origin.
b) B: (-3,-5), C: (5,-2)
c) (3,-4)