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Chapter 1: Problem 33

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$(-1,2),(5,4)$$

Short Answer

Expert verified
The plotted points are (-1,2) and (5,4). The distance between the points is 鈭�40. The midpoint of the line segment joining the points is (2, 3).

Step by step solution

01

Plotting the points

Second, plot the points (-1,2) and (5,4) on the coordinate plane. The first value in each pair is the x-coordinate and the second is the y-coordinate.
02

Finding the distance between the points

Next, find the distance between the two points. Use the distance formula which is 鈭歔(x鈧� - x鈧�)虏 + (y鈧� - y鈧�)虏. Substituting the given points into the formula gives: 鈭歔(5 - -1)虏 + (4 - 2)虏] = 鈭歔(5 + 1)虏 + (4 - 2)虏] = 鈭歔6虏 + 2虏] = 鈭歔36 + 4] = 鈭�40.
03

Finding the midpoint of the line segment

Finally, find the midpoint of the line segment joining the points using the midpoint formula: [(x鈧�+x鈧�)/2 , (y鈧�+y鈧�)/2]. Substituting the given points into the formula gives: [(-1 + 5)/2 , (2 + 4)/2] = [2, 3]. So, the midpoint is (2, 3).

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