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Chapter 1: Problem 35

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$(-16.8,12.3),(5.6,4.9)$$

Short Answer

Expert verified
The distance between the points A(-16.8, 12.3) and B(5.6, 4.9) is approximately 23.6 units. The midpoint of the line segment joining these points is (-5.6, 8.6).

Step by step solution

01

Plot the Points

Plot the provided points (-16.8, 12.3) and (5.6, 4.9) on a Cartesian plane. These will be represented as A(-16.8, 12.3) and B(5.6, 4.9).
02

Calculate the Distance between the Points

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) where \(x_1, y_1)\) and \(x_2, y_2)\) are the coordinates of point A and B respectively. Substituting the given values, we get \(d = \sqrt{(5.6 - -16.8)^2 + (4.9 - 12.3)^2}\)
03

Simplify the Distance Result

Solving the square roots under the square root gets \(d = \sqrt{(22.4)^2 + (-7.4)^2} = \sqrt{(501.76) + (54.76)} = \sqrt{(556.52)}\)
04

Calculate the Midpoint of the Line Segment

Use the midpoint formula \((\(\frac{x1 + x2}{2}, \frac{y1 + y2}{2})\) where \(x_1, y_1\) and \(x_2, y_2\) are the coordinates of point A and B respectively. Substituting the given values, we get \(M = (\frac{-16.8 + 5.6}{2}, \frac{12.3 + 4.9}{2})\)
05

Simplify the Midpoints

Solve the respective fraction to get \(M = (-5.6, 8.6)\)

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