Chapter 13.1, Problem 5CE

a.

To determine

To find the coordinates of T

Answer to Problem 5CE

The value of T is $\left(7,2\right)$

Explanation of Solution

Given information:

Looking at the graph given in the question

The given points is

  $\left(-1,2\right)\text{ and }\left(7,5\right)$

Calculation:

The coordinates of T can be obtained as

The point T lies on the horizontal line of $\left(-1,2\right)$ and vertical line of $\left(7,5\right)$

Let $\left(x_1,y_1\right)\text{ be }\left(-1,2\right)\text{ and }\left(x_2,y_2\right)\text{ be }\left(7,5\right)$

Than the point T is $\left(x_2,y_1\right)=\left(7,2\right)$

Hence,

The value of T is $\left(7,2\right)$

b.

To determine

To find the length of the legs of the right triangle

Answer to Problem 5CE

The value of legs are $\left(8,3\right)$

Explanation of Solution

Given information:

Looking at the graph given in the question

The given points is

  $\left(-1,2\right)\text{ and }\left(7,5\right)$

Calculation:

The length of the legs of the right triangle can be obtained as

The point T lies on the horizontal line of $\left(-1,2\right)$ and vertical line of $\left(7,5\right)$

Let $\left(x_1,y_1\right)\text{ be }\left(-1,2\right)\text{ and }\left(x_2,y_2\right)\text{ be }\left(7,5\right)$

Than,

  $\begin{array}{l}\left(x_2-x_1\right)=\left(7-\left(-1\right)\right)\text{ and }\left(y_2-y_1\right)=\left(5-2\right)\\ \left(x_2-x_1\right)=\left(7+1\right)\left(y_2-y_1\right)=3\\ \left(x_2-x_1\right)=8\end{array}$

Hence,

The value of legs are $\left(8,3\right)$

c.

To determine

To find the length of the segment

Answer to Problem 5CE

The value of the length of the segment are $\sqrt{73}$

Explanation of Solution

Given information:

Looking at the graph given in the question

The given points is

  $\left(-1,2\right)\text{ and }\left(7,5\right)$

Calculation:

The length of the segment can be obtained as

The point T lies on the horizontal line of $\left(-1,2\right)$ and vertical line of $\left(7,5\right)$

Let $\left(x_1,y_1\right)\text{ be }\left(-1,2\right)\text{ and }\left(x_2,y_2\right)\text{ be }\left(7,5\right)$

Use the distance formula between the two points to find the segment

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\left[d=\text{distance}\right]\\ d=\sqrt{{\left(7-\left(-1\right)\right)}^2+{\left(5-2\right)}^2}\\ d=\sqrt{{\left(7+1\right)}^2+{\left(3\right)}^2}\\ d=\sqrt{{\left(8\right)}^2+{\left(3\right)}^2}\\ d=\sqrt{64+9}\\ d=\sqrt{73}\end{array}$

Hence,

The value of the length of the segment are $\sqrt{73}$