Chapter 13.1, Problem 15PSB

(a)

To determine

To find: The coordinates of vertex $B$ .

Answer to Problem 15PSB

The coordinates of $\text{B}$ is $\left(2,5\right)$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

The longer base intercepts the y-axis at its midpoint (by midpoint formula), so the shorter base must also if the trapezoidal is isosceles. So, the coordinates of $\text{B}$ is $\left(0+2,5\right)$ or $\left(2,5\right)$ .

Therefore, the coordinates of $\text{B}$ is $\left(2,5\right)$ .

(b)

To determine

To find: The length of the bases.

Answer to Problem 15PSB

The lengths of bases are 4 and 14.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the length of the shorter base as follows.

  $\begin{array}{c}{l}_1=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}\\ =\sqrt{{\left(-2-2\right)}^2+{\left(5-5\right)}^2}\\ =\sqrt{{\left(-4\right)}^2}\\ =4\end{array}$

Find the length of the longer base as follows.

  $\begin{array}{c}{l}_1=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}\\ =\sqrt{{\left(-7-7\right)}^2+{\left(-2+2\right)}^2}\\ =\sqrt{{\left(-14\right)}^2}\\ =14\end{array}$

Therefore, the length of bases are 4 and 14.

(c)

To determine

To find: The length of the median.

Answer to Problem 15PSB

The length of the median to the hypotenuse is $2.5$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the length of median as follows.

  $\begin{array}{c}M=\frac{1}{2}\left(l_1+l_2\right)\\ =\frac{1}{2}\left(4+14\right)\\ =\frac{18}{2}\\ =9\end{array}$

Therefore, the length of the median is $9$ .

(d)

To determine

To find: The area of the trapezoid.

Answer to Problem 15PSB

The area of the trapezoid is $63$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the area of trapezoid as follows.

  $\begin{array}{c}A=\frac{1}{2}\left(\text{sum}\text{of}\text{two}\text{parallel}\text{sides}\right)\times \left(\text{height}\right)\\ =\frac{1}{2}\left(4+14\right)\times 7\\ =\frac{18}{2}\times 7\\ =63\end{array}$

Therefore, the area of the trapezoid is $63$ .