Hint: Create a right triangle, then use the Pythagorean Theorem.Ģ2. Plot the points A(−3, −3) and B(0, 0) and find the straight-line distance between the two points. Plot these points, draw the triangle ABC, then compute the area of the triangle ABC.Ģ1. The points A(−2, −3), B(−1, −3), and C(−2, 1) are the vertices of a triangle. Plot these points, draw the triangle ABC, then compute the area of the triangle ABC.Ģ0. The points A(−1, −2), B(0, −2), and C(−1, 0) are the vertices of a triangle. Plot these points, draw the triangle ABC, then compute the area of the triangle ABC.ġ9. The points A(−3, −2), B(1, −2), and C(−3, 2) are the vertices of a triangle. Plot these points, draw the triangle ABC, then compute the area of the triangle ABC.ġ8. The points A(−3, −1), B(1, −1), and C(−3, 0) are the vertices of a triangle. Plot these points, draw the rectangle ABCD, then compute the perimeter of rectangle ABCD.ġ7. The points A(−4, 2), B(3, 2), C(3, 4), and D(−4, 4) are the vertices of a rectangle. Plot these points, draw the rectangle ABCD, then compute the perimeter of rectangle ABCD.ġ6. The points A(−1, 2), B(3, 2), C(3, 3), and D(−1, 3) are the vertices of a rectangle. Plot these points, draw the rectangle ABCD, then compute the perimeter of rectangle ABCD.ġ5. Plot these points, draw the rectangle ABCD, then compute the perimeter of rectangle ABCD.ġ4. Plot these points, draw the rectangle ABCD, then compute the area of rectangle ABCD.ġ3. Plot these points, draw the rectangle ABCD, then compute the area of rectangle ABCD.ġ2. Plot these points, draw the rectangle ABCD, then compute the area of rectangle ABCD.ġ1. Plot these points, draw the rectangle ABCD, then compute the area of rectangle ABCD.ġ0. The points A(−1, 1), B(1, 1), C(1, 2), and D(−1, 2) are the vertices of a rectangle. Identify the coordinates of the point P.ĩ. Identify the coordinates of the point P.Ĩ. Identify the coordinates of the point P.ħ. Identify the coordinates of the point P.Ħ. Identify the coordinates of the point P.ĥ. Identify the coordinates of the point P.Ĥ. Identify the coordinates of the point P.ģ. Identify the coordinates of the point P.Ģ. Instead, you should work on graph paper.ġ. However, you do not have to draw these gridlines yourself. The grid in Figure 8.3(b) is a visualization that greatly eases the plotting of ordered pairs. The combination of axes and grid in Figure 8.3(b) is called a coordinate system. The second number is called the ordinate and measures the vertical distance to the plotted point. The first number of the ordered pair is called the abscissa and measures the horizontal distance to the plotted point. The numbers in the ordered pair (5, 6) are called the coordinates of the plotted point in Figure 8.3(b). Figure 8.3: Plotting the Point (5, 6) in a Cartesian Coordinate System. Adding a grid of horizontal and vertical lines at each whole number makes plotting the point (5, 6) much clearer, as shown in Figure 8.3(b). To plot this point on the “coordinate system” in Figure 8.3(a), start at the origin (0, 0), then move 5 units in the horizontal direction, then 6 units in the vertical direction, then plot a point. Now, consider the ordered pair of whole numbers (5, 6). Figure 8.2: A Cartesian coordinate system. The resulting construct is an example of a Cartesian Coordinate System. The point where the zero locations touch is called the origin of the coordinate system and has coordinates (0, 0). To plot ordered pairs, we need two number lines, called the horizontal and vertical axes, that intersect at the zero location of each line and are at right angles to one another, as shown in Figure 8.2(a). Figure 8.1: Plotting the whole numbers 2, 5, and 7 on a number line. For example, in Figure 8.1, we’ve plotted the whole numbers 2, 5, and 7 as shaded “dots” on the number line. We’ve seen how to plot whole numbers on a number line. Consequently, the ordered pair ( x, y) is not the same as the ordered pair ( y, x), because the numbers are presented in a different order. Pay particular attention to the phrase “ordered pairs.” Order matters.
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