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Chapter 1: Problem 47

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$ (1,1),(9,7) $$

Short Answer

Expert verified
The distance between the points (1,1) and (9,7) is 10 units. The midpoint of the line segment joining these points is (5,4).

Step by step solution

01

Plotting the points

Plot the two points (1,1) and (9,7) on a graph.
02

Calculating the distance between the points

Apply the distance formula \[d = \sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\] Where (x1, y1) and (x2, y2) are the coordinates of two points. Substituting the given coordinates, we find: \[ d = \sqrt {(9-1)^{2}+(7-1)^{2}} = 10 \] So, the distance between the two points is 10 units.
03

Finding the Midpoint of the Line Segment

Apply the midpoint formula \[ M = \left(\frac{(x_{1}+x_{2})}{2}, \frac{(y_{1}+y_{2})}{2}\right) \] Substitute the given coordinates, we find: \[ M = \left(\frac{(1+9)}{2}, \frac{(1+7)}{2}\right) = (5,4) \] So, the midpoint of the line segment joining the points (1,1) and (9,7) is (5,4).

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Use the given value of \(k\) to complete the table for the inverse variation model $$y=\frac{k}{x^{2}}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=\frac{k}{x^{2}} & & & & & \\ \hline \end{array}$$ $$ k=5 $$

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