Question

2 - 40. one of the topics you will review in this course is reading graphs. look at the graph at right. this graph shows positive and negative values on both axes. it divides the flat surface into four parts, or quadrants, and is therefore 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 - system concept

In a two - dimensional coordinate system, the first number in an ordered pair $(x,y)$ is the $x$ - coordinate (horizontal position) and the second is the $y$ - coordinate (vertical position). For point $A(-3,5)$, the $x$ - coordinate $x=-3$ means the point is 3 units to the left of the origin (since $x < 0$), and the $y$ - coordinate $y = 5$ means the point is 5 units above the origin (since $y>0$).

Step2: Find coordinates of $B$ and $C$

For 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 $(-3,-5)$. For point $C$, it is 6 units to the right of the origin ($x = 6$) and 2 units below the origin ($y=-2$), so the coordinates of $C$ are $(6,-2)$.

Step3: Calculate new position of $A$

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

Answer:

a. The $x$ - coordinate $x=-3$ means the point is 3 units to the left of the origin and the $y$ - coordinate $y = 5$ means the point is 5 units above the origin.
b. $B(-3,-5)$, $C(6,-2)$
c. $(3,-4)$