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Chapter 1: Problem 36

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$\left(\frac{1}{2}, 1\right),\left(-\frac{5}{2}, \frac{4}{3}\right)$$

Short Answer

Expert verified
The points (1/2, 1) and (-5/2, 4/3) plotted on a Cartesian grid shows the points are in the first and second quadrant respectively. By substituting the given points in the distance formula, the distance between the points is calculated to be \(5\sqrt{13}/6\) units. The midpoint of the line segment joining the points is obtained by averaging the respective coordinates, which gives the solution as (-1, 11/6).

Step by step solution

01

Plotting the Points

Plot the given coordinates (1/2, 1), and (-5/2, 4/3) on a graph. Position the horizontal axis and the vertical axis, (1/2, 1) will be in the first quadrant and point (-5/2, 4/3) will be in the second quadrant.
02

Calculation of the Distance between the Points

The distance between two points (x1,y1) and (x2,y2) is given by the distance formula \(d = \sqrt{{(x2-x1)^2 + (y2-y1)^2}}\). Replace x1, y1, x2, y2 with 1/2, 1, -5/2, 4/3 respectively in the formula and calculate the result.
03

Finding the Midpoint

The midpoint of a line segment with endpoints (x1,y1) and (x2,y2) is given by \(( (x1+x2)/2, (y1+y2)/2 )\). Replace x1, y1, x2, y2 with 1/2, 1, -5/2, 4/3 respectively in the formula and calculate the result. This will yield the coordinates of the midpoint.

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