Question 2.1.1: Plot the points A(-3, 6) and B(5, 1), and find the distance ......
Plot the points A(-3, 6) and B(5, 1), and find the distance d(A, B).
Point A: (-3, 6)
Point B: (5, 1)
Step 1:
Identify the coordinates of points A and B. In this case, point A has coordinates (-3, 6) and point B has coordinates (5, 1).
Step 2:
Use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Step 3:
Substitute the coordinates of points A and B into the distance formula: d = sqrt((5 - (-3))^2 + (1 - 6)^2)
Step 4:
Simplify the expression inside the square root: d = sqrt((8)^2 + (-5)^2)
Step 5:
Calculate the values inside the square root: d = sqrt(64 + 25)
Step 6:
Add the values inside the square root: d = sqrt(89)
Step 7:
Approximate the square root of 89: d ≈ 9.43
Step 8:
Therefore, the distance between points A and B is approximately 9.43 units.
Final Answer
The points are plotted in Figure 4. By the distance formula,
\begin{aligned}d(A, B) & =\sqrt{[5-(-3)]^2+(1-6)^2} \\& =\sqrt{8^2+(-5)^2} \\& =\sqrt{64+25}=\sqrt{89} \approx 9.43 .\end{aligned}
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