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Chapter 1: Problem 48

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$ (1,12),(6,0) $$

Short Answer

Expert verified
The distance between the points (1,12) and (6,0) is 13 units. The midpoint of the line segment joining these points is (3.5,6).

Step by step solution

01

Plotting the Points (1,12) and (6,0)

To plot these points, locate the first number of each pair on the x-axis and the second number on the y-axis. Point (1,12) is 1 unit to the right and 12 units up from the origin. Similarly, point (6,0) is 6 units to the right of the origin along the horizontal axis.
02

Calculate the Distance Between the Points

The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) in a cartesian plane is given by the formula \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\). Substituting the values \(x_1 = 1, y_1 = 12, x_2 = 6, y_2 = 0\) we find that \(d = \sqrt{(6-1)^2 + (0-12)^2} = \sqrt{25+144} = \sqrt{169} = 13\).
03

Find the Midpoint of the Line Segment Joining the Points

The midpoint of two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Substituting the given values \(x_1 = 1, y_1 = 12, x_2 = 6, y_2 = 0\) we get \((\frac{1 + 6}{2},\frac{12 + 0}{2}) = (3.5, 6)\).

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