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Chapter 1: Problem 53

(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 plotted points, distance between them and their midpoint have been computed.

Step by step solution

01

- Plot the points

Plot the points \(\left(\frac{1}{2}, 1\right)\) and \(\left(-\frac{5}{2}, \frac{4}{3}\right)\) on a coordinate plane.
02

- Distance formula

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane is given by the formula: \[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]. Using the provided points, the distance becomes: \[d = \sqrt{(-\frac{5}{2}-\frac{1}{2})^2 + (\frac{4}{3}-1)^2} \]. Simplify this expression to find the numerical value of d.
03

- Midpoint formula

The midpoint between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula \[\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\]. Using the provided points, the midpoint becomes \[\left(\frac{\frac{1}{2} -\frac{5}{2}}{2}, \frac{1+\frac{4}{3}}{2}\right)\]. Simplify this expression to find the coordinates of the midpoint.

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