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Chapter 1: Problem 29

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$(6,-3),(6,5)$$

Short Answer

Expert verified
The points (6,-3) and (6,5) are plotted on a two-dimensional plane. The distance between these points is 8 units, and the midpoint of the line segment joining these points is (6,1).

Step by step solution

01

Plot the Points

The first point to plot is (6,-3). The x-coordinate is 6 and the y-coordinate is -3. The second point to plot is (6,5), where 6 is the x-coordinate and 5 is the y-coordinate. We plot these points on a two dimensional plane, where the horizontal axis represents x-coordinate and the vertical axis represents y-coordinate.
02

Find the Distance

To find the distance between the points, we apply the distance formula: \(d= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Here, (x1, y1) and (x2, y2) are the coordinates of the given points. In our case, x1 = x2 = 6, and y1 = -3, y2 = 5. Substituting these values into the formula: \(d= \sqrt{(6 - 6)^2 + (5 - (-3))^2}\) = \(\sqrt{0 + 64}\) = 8.
03

Find the Midpoint

The midpoint of a line segment is found using the formula: \(M= ((x_1 + x_2)/2 , (y_1 + y_2)/2)\), where (x1, y1) and (x2, y2) are the end points. For the given points, x1 = x2 = 6 and y1 = -3, y2 = 5. Substituting these values into the formula: \(M= ((6 + 6)/2 , (-3 + 5)/2)\) = (6, 1).

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