Chapter 1.8, Problem 8E

To determine

To calculate: The coordinates of the points from the figure provided below,

  

Answer to Problem 8E

The coordinates of the points are,

  $\begin{array}{cc}\text{Point}& \text{Coordinate}\\ A& \left(5,1\right)\\ B& \left(1,2\right)\\ C& \left(-2,6\right)\\ D& \left(-6,2\right)\\ E& \left(-4,-1\right)\\ F& \left(-2,0\right)\\ G& \left(-1,-3\right)\\ H& \left(2,-2\right)\end{array}$

Explanation of Solution

Given information:

The points are marked in the Cartesian plane

  

Formula used:

The Cartesian plane is divided into four quadrant. Numbers on right of zero are positive, on left of zero are negative. Numbers above zero on vertical line are positive and numbers below 0 are negative. Each pair of point in the coordinate plane is represented as an ordered pair $\left(x,y\right)$ where first element is the x-coordinate and second element is the y-coordinate. The point $\left(x,y\right)$ denote it is x units on x-axis and y units on y −axis and marked accordingly.

Calculation:

Consider the provided points that are marked in the Cartesian plane

  

Observe that the Cartesian plane is divided into four quadrant. Numbers on right of zero are positive, on left of zero are negative. Numbers above zero on vertical line are positive and numbers below 0 are negative. Each pair of point in the coordinate plane is represented as an ordered pair $\left(x,y\right)$ where first element is the x-coordinate and second element is the y-coordinate. The point $\left(x,y\right)$ denote it is x units on x-axis and y units on y −axis and marked accordingly.

For the point $A$ , x-coordinate is 5 and y-coordinate is 1.

For the point $B$ , x-coordinate is 1 and y-coordinate is 2.

For the point $C$ , x-coordinate is $-2$ and y-coordinate is 6.

For the point $D$ , x-coordinate is $-6$ and y-coordinate is 2.

For the point $E$ , x-coordinate is $-4$ and y-coordinate is $-1$ .

For the point $F$ , x-coordinate is $-2$ and y-coordinate is 1.

For the point $G$ , x-coordinate is $-1$ and y-coordinate is $-3$ .

For the point $H$ , x-coordinate is $2$ and y-coordinate is $-2$ .

Therefore, the coordinates of points is tabulated as,

  $\begin{array}{cc}\text{Point}& \text{Coordinate}\\ A& \left(5,1\right)\\ B& \left(1,2\right)\\ C& \left(-2,6\right)\\ D& \left(-6,2\right)\\ E& \left(-4,-1\right)\\ F& \left(-2,0\right)\\ G& \left(-1,-3\right)\\ H& \left(2,-2\right)\end{array}$